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Aug
26
comment Kaplansky characterization of principal Artin ring
@Jim You don't see "share edit close delete flag protect" immediately below the tags on your post?
Aug
26
comment Is there a binary operator (besides composition) closed under permutations or a notion of a metric space on permutations?
@bulletninja What behavior specifically?
Aug
26
revised Example of a commutative perfect ring that is not artinian
added 668 characters in body
Aug
26
comment Example of a commutative perfect ring that is not artinian
Dear @JasonJuett : that characterization is not correct. an infinite product of fields is both zero dimensional and has radical zero, but is not perfect. But of course you're spot on that commutative perfect rings are zero dimensional. Regards
Aug
25
comment Kaplansky characterization of principal Artin ring
@Jim I thought a poster could self delete no matter what reputation.
Aug
25
answered Converse of “localization at a prime is local”
Aug
24
comment Number of Idempotent matrices.
Are you saying the matrices are over the field of two elements, or do you just mean matrices over whatever field?
Aug
24
comment Can an element in a Noetherian ring have arbitrarily long factorizations?
I could duplicate information that appears in better-asked questions elsewhere, but that would not be a good use of time, especially considering that is not the main question here. I've provided a link, though, to fill the reference you broke when moving your solution. Regards.
Aug
24
revised Can an element in a Noetherian ring have arbitrarily long factorizations?
added 186 characters in body
Aug
23
answered Can an element in a Noetherian ring have arbitrarily long factorizations?
Aug
22
comment How to find prime ideals of $3\Bbb Z$?
@mwomath $3\Bbb Z/9\Bbb Z$ is a three element ring in which all elements square to zero: it is not $\Bbb Z_3$ at all.
Aug
21
revised In algebraic topology, for a function $f$ what does $f _\ast$ mean?
ce
Aug
21
comment Is there a binary operator (besides composition) closed under permutations or a notion of a metric space on permutations?
What do you mean "additive operation"?
Aug
21
answered Is there a binary operator (besides composition) closed under permutations or a notion of a metric space on permutations?
Aug
21
comment If $R_1,..$ are rings with identity and $I$ is an ideal in $R_1\times.. R_n$, then $I=A_1\times…\times A_m$,where each $A_i$ is an ideal in $R_i$.
@haiganghu might be worth answering your own question to explain what you realized then!
Aug
20
comment If $R_1,..$ are rings with identity and $I$ is an ideal in $R_1\times.. R_n$, then $I=A_1\times…\times A_m$,where each $A_i$ is an ideal in $R_i$.
Until you write how you "can get $I$ has the form $A_1\times...\times A_m$" we can't know for sure if you have done it without using identities. It is certainly easy if you are given identities.
Aug
19
answered Can we construct a homomorphism from a projective module into a free module?
Aug
19
comment Adjoining an identity to a ring
It's a neat little exercise. What algebra book was it, btw?
Aug
19
comment Adjoining an identity to a ring
@karparvar that also explains why $(0, R_0)$ does collapse to zero when localizing at any prime containing $R_0$ :)
Aug
19
comment Adjoining an identity to a ring
@karparvar Ah ok, e would definitely be zero in the localization, yes.