Handbook of basic algebra
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Similarly to how an analyst may be looking for an analysis handbook listing the general solutions to different integrals (as for example in Schaum's Mathematical Handbook of Formulas and Tables does) I am looking for a handbook on basic (Groups, Rings, Vector Spaces, Modules,...- nothing fancy) algebra that systematically (!) states facts about how certain properties behave w.r.t. basic constructions.
The answers to some of those types of questions are well known, because they are so important (eg. Hilbert Basis Theorem: $R$ noetherian $Rightarrow$ $R[X]$ noetherian). Some are easy to remember (e.g. the product of an integral domain is not in general an integral domain). Others, however, are neither, but still arise from time to time, when trying to prove something (e.g. in a UFD, is a ring prime if and only if every element of its minimal generating set if prime?). In other words: A list of lemmas (not even necessarily with proofs) stating natural (!) assertions.
For example, in such a book one may find a table for rings where the column-heads are classifying conditions of rings (such as Integral Domain, Principal Ideal Domain, Reduced, ...) and in the row-heads basic constructions (such as Product, Subring, Intersection, ...) and every cell says "true" if the [construction] of a ring with [property] has [property]" and "false" if not.
Something similar to maybe nLab for Category Theory or Groupprops for Group Theory. Note though, that neither is a precise analogy to what I'm looking for. Everything I have found yet is either much close to a textbook states too few theorem or in a (seemingly) non-systematic manner.
Let me repeat, I am not looking for a textbook, but a handbook; somewhat similar to how an engineer may use a handbook on mechanics.
Now, my question: Does anybody know of a book or website of that type? Or have any other comments?
abstract-algebra reference-request commutative-algebra
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
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add a comment |
$begingroup$
Similarly to how an analyst may be looking for an analysis handbook listing the general solutions to different integrals (as for example in Schaum's Mathematical Handbook of Formulas and Tables does) I am looking for a handbook on basic (Groups, Rings, Vector Spaces, Modules,...- nothing fancy) algebra that systematically (!) states facts about how certain properties behave w.r.t. basic constructions.
The answers to some of those types of questions are well known, because they are so important (eg. Hilbert Basis Theorem: $R$ noetherian $Rightarrow$ $R[X]$ noetherian). Some are easy to remember (e.g. the product of an integral domain is not in general an integral domain). Others, however, are neither, but still arise from time to time, when trying to prove something (e.g. in a UFD, is a ring prime if and only if every element of its minimal generating set if prime?). In other words: A list of lemmas (not even necessarily with proofs) stating natural (!) assertions.
For example, in such a book one may find a table for rings where the column-heads are classifying conditions of rings (such as Integral Domain, Principal Ideal Domain, Reduced, ...) and in the row-heads basic constructions (such as Product, Subring, Intersection, ...) and every cell says "true" if the [construction] of a ring with [property] has [property]" and "false" if not.
Something similar to maybe nLab for Category Theory or Groupprops for Group Theory. Note though, that neither is a precise analogy to what I'm looking for. Everything I have found yet is either much close to a textbook states too few theorem or in a (seemingly) non-systematic manner.
Let me repeat, I am not looking for a textbook, but a handbook; somewhat similar to how an engineer may use a handbook on mechanics.
Now, my question: Does anybody know of a book or website of that type? Or have any other comments?
abstract-algebra reference-request commutative-algebra
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
$endgroup$
$begingroup$
I'm trying to do something like this for rings at the Database of ring theory but currently that section is only in its beginnings. Suggestions for additions are appreciated.
$endgroup$
– rschwieb
Dec 12 '18 at 14:18
$begingroup$
@rschwieb Yes!! That's great. Indeed, rings and commutative algebra were my primary motivation for this question.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:31
$begingroup$
Well, I look forward to hearing your input and feedback :)
$endgroup$
– rschwieb
Dec 12 '18 at 14:44
add a comment |
$begingroup$
Similarly to how an analyst may be looking for an analysis handbook listing the general solutions to different integrals (as for example in Schaum's Mathematical Handbook of Formulas and Tables does) I am looking for a handbook on basic (Groups, Rings, Vector Spaces, Modules,...- nothing fancy) algebra that systematically (!) states facts about how certain properties behave w.r.t. basic constructions.
The answers to some of those types of questions are well known, because they are so important (eg. Hilbert Basis Theorem: $R$ noetherian $Rightarrow$ $R[X]$ noetherian). Some are easy to remember (e.g. the product of an integral domain is not in general an integral domain). Others, however, are neither, but still arise from time to time, when trying to prove something (e.g. in a UFD, is a ring prime if and only if every element of its minimal generating set if prime?). In other words: A list of lemmas (not even necessarily with proofs) stating natural (!) assertions.
For example, in such a book one may find a table for rings where the column-heads are classifying conditions of rings (such as Integral Domain, Principal Ideal Domain, Reduced, ...) and in the row-heads basic constructions (such as Product, Subring, Intersection, ...) and every cell says "true" if the [construction] of a ring with [property] has [property]" and "false" if not.
Something similar to maybe nLab for Category Theory or Groupprops for Group Theory. Note though, that neither is a precise analogy to what I'm looking for. Everything I have found yet is either much close to a textbook states too few theorem or in a (seemingly) non-systematic manner.
Let me repeat, I am not looking for a textbook, but a handbook; somewhat similar to how an engineer may use a handbook on mechanics.
Now, my question: Does anybody know of a book or website of that type? Or have any other comments?
abstract-algebra reference-request commutative-algebra
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
$endgroup$
Similarly to how an analyst may be looking for an analysis handbook listing the general solutions to different integrals (as for example in Schaum's Mathematical Handbook of Formulas and Tables does) I am looking for a handbook on basic (Groups, Rings, Vector Spaces, Modules,...- nothing fancy) algebra that systematically (!) states facts about how certain properties behave w.r.t. basic constructions.
The answers to some of those types of questions are well known, because they are so important (eg. Hilbert Basis Theorem: $R$ noetherian $Rightarrow$ $R[X]$ noetherian). Some are easy to remember (e.g. the product of an integral domain is not in general an integral domain). Others, however, are neither, but still arise from time to time, when trying to prove something (e.g. in a UFD, is a ring prime if and only if every element of its minimal generating set if prime?). In other words: A list of lemmas (not even necessarily with proofs) stating natural (!) assertions.
For example, in such a book one may find a table for rings where the column-heads are classifying conditions of rings (such as Integral Domain, Principal Ideal Domain, Reduced, ...) and in the row-heads basic constructions (such as Product, Subring, Intersection, ...) and every cell says "true" if the [construction] of a ring with [property] has [property]" and "false" if not.
Something similar to maybe nLab for Category Theory or Groupprops for Group Theory. Note though, that neither is a precise analogy to what I'm looking for. Everything I have found yet is either much close to a textbook states too few theorem or in a (seemingly) non-systematic manner.
Let me repeat, I am not looking for a textbook, but a handbook; somewhat similar to how an engineer may use a handbook on mechanics.
Now, my question: Does anybody know of a book or website of that type? Or have any other comments?
abstract-algebra reference-request commutative-algebra
abstract-algebra reference-request commutative-algebra
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
asked Dec 12 '18 at 14:09
G. ChiusoleG. Chiusole
1639
1639
$begingroup$
I'm trying to do something like this for rings at the Database of ring theory but currently that section is only in its beginnings. Suggestions for additions are appreciated.
$endgroup$
– rschwieb
Dec 12 '18 at 14:18
$begingroup$
@rschwieb Yes!! That's great. Indeed, rings and commutative algebra were my primary motivation for this question.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:31
$begingroup$
Well, I look forward to hearing your input and feedback :)
$endgroup$
– rschwieb
Dec 12 '18 at 14:44
add a comment |
$begingroup$
I'm trying to do something like this for rings at the Database of ring theory but currently that section is only in its beginnings. Suggestions for additions are appreciated.
$endgroup$
– rschwieb
Dec 12 '18 at 14:18
$begingroup$
@rschwieb Yes!! That's great. Indeed, rings and commutative algebra were my primary motivation for this question.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:31
$begingroup$
Well, I look forward to hearing your input and feedback :)
$endgroup$
– rschwieb
Dec 12 '18 at 14:44
$begingroup$
I'm trying to do something like this for rings at the Database of ring theory but currently that section is only in its beginnings. Suggestions for additions are appreciated.
$endgroup$
– rschwieb
Dec 12 '18 at 14:18
$begingroup$
I'm trying to do something like this for rings at the Database of ring theory but currently that section is only in its beginnings. Suggestions for additions are appreciated.
$endgroup$
– rschwieb
Dec 12 '18 at 14:18
$begingroup$
@rschwieb Yes!! That's great. Indeed, rings and commutative algebra were my primary motivation for this question.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:31
$begingroup$
@rschwieb Yes!! That's great. Indeed, rings and commutative algebra were my primary motivation for this question.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:31
$begingroup$
Well, I look forward to hearing your input and feedback :)
$endgroup$
– rschwieb
Dec 12 '18 at 14:44
$begingroup$
Well, I look forward to hearing your input and feedback :)
$endgroup$
– rschwieb
Dec 12 '18 at 14:44
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
One example is the book series
Handbook of Algebra,
edited by M. Hazewinkel.
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
$endgroup$
$begingroup$
True, but this is unfortunately an example for those books that are more like a textbook, and less like a database.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:22
add a comment |
Your Answer
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1 Answer
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1 Answer
1
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oldest
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$begingroup$
One example is the book series
Handbook of Algebra,
edited by M. Hazewinkel.
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
$endgroup$
$begingroup$
True, but this is unfortunately an example for those books that are more like a textbook, and less like a database.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:22
add a comment |
$begingroup$
One example is the book series
Handbook of Algebra,
edited by M. Hazewinkel.
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
$endgroup$
$begingroup$
True, but this is unfortunately an example for those books that are more like a textbook, and less like a database.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:22
add a comment |
$begingroup$
One example is the book series
Handbook of Algebra,
edited by M. Hazewinkel.
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
$endgroup$
One example is the book series
Handbook of Algebra,
edited by M. Hazewinkel.
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
answered Dec 12 '18 at 14:12
Dietrich BurdeDietrich Burde
79.8k647103
79.8k647103
$begingroup$
True, but this is unfortunately an example for those books that are more like a textbook, and less like a database.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:22
add a comment |
$begingroup$
True, but this is unfortunately an example for those books that are more like a textbook, and less like a database.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:22
$begingroup$
True, but this is unfortunately an example for those books that are more like a textbook, and less like a database.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:22
$begingroup$
True, but this is unfortunately an example for those books that are more like a textbook, and less like a database.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:22
add a comment |
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$begingroup$
I'm trying to do something like this for rings at the Database of ring theory but currently that section is only in its beginnings. Suggestions for additions are appreciated.
$endgroup$
– rschwieb
Dec 12 '18 at 14:18
$begingroup$
@rschwieb Yes!! That's great. Indeed, rings and commutative algebra were my primary motivation for this question.
$endgroup$
– G. Chiusole
Dec 12 '18 at 14:31
$begingroup$
Well, I look forward to hearing your input and feedback :)
$endgroup$
– rschwieb
Dec 12 '18 at 14:44