Related papers: Categorical rings subsume ann-categories
We present two criteria for a group $G$ to satisfy the following statements: any $G$-graded gr-prime (gr-semiprime) right gr-Goldie ring admits a gr-semisimple graded right classical quotient ring. The criterion for gr-semiprime rings is…
This paper has been withdrawn by the author because the conclusions reached in it are incorrect.
This paper has been withdrawn by the author. The statement of the Main Theorem but is wrong in general, there have been provided counterexamples. The main theorem only holds conditionally, under the finiteness statement of theorem 2.8.
This paper has been withdrawn by the authors due to inadequate arguments.
This paper has been withdrawn by the author due to an error in the proof.
This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.
This paper has been withdrawn by the author due to the incorrect argument for the security.
We prove a general divisibility theorem that implies, e.g., that, in any group, the number of generating pairs (as well as triples, etc.) is a multiple of the order of the commutator subgroup. Another corollary says that, in any associative…
This paper has been withdrawn by the author due to a gap in the proof of the main result.
I withdraw my paper from arXiv because there is a technical error in the proof of Theorem 1.1. And because of this error, all the results in the paper are untrue. I am very sorry for this.
We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…
This paper has been withdrawn by the authors, since it has been merged with Part I (ID 0802.3570)
This paper has been withdrawn to address an omission. It will be resubmitted in the near future.
Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full…
Withdrawn due to error. See D. Lowe, L. Susskind and J. Uglum, hep-th/9402136, for correct treatment. Apologies to all recipients.
This paper has been withdrawn by the author [arXiv admin].
Withdrawn paper because the results are published in math.AT/0308054 and math.AT/0308063.
This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.
We define here the notion of a {\it weakly reversible ring} $R$ saying that a non-zero element $a\in R$ is weakly reversible if there exists an integer $m>0$ depending on $a$ such that $a^m\neq 0$ is reversible, that is,…
This paper has been withdrawn by the author.