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Results tagged with graded-rings-modules
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user 85967
8
votes
Accepted
$\mathbb{Z}$-graded algebras and tensor products
No it cannot happen.
And not only for strongly $\mathbb{Z}$-graded rings; this is always the case for any strongly $G$-graded ring, where $G$ is a group. $A_k \otimes_{A_0} A_l \simeq A_{k+l}$ is an i …
- 7,746
4
votes
Accepted
Strongly graded algebras with no zero divisors
Yes this is always an isomorphism of $A_0$-bimodules.
It is a general result for strongly graded rings. It holds for an arbitrary grading group $G$ (not necessarily $\mathbb{Z}$) and does not depend …
- 7,746
3
votes
Conceptual explanation for the sign in front of some binary operations
I find the question quite interesting (in the sense that similar questions related to sign factors appearing in various different algebraic structures with no apparent reason, have been going through …
- 7,746
2
votes
Graded analogues of theorems in commutative algebra
Since the OP is asking for some "class of statements" which can be readily transferred from the ungraded to the graded case, let me outline a couple of thoughts, which are not really tied to neither …
1
vote
Representation theory in braided monoidal categories
I will try to provide an answer for a particular case of your last question: Let us consider (following my comment above) the case of $H=\mathbb{CZ}_2$ i.e. the group hopf algebra equipped with its no …
- 7,746