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A generalization of the Auslander transpose and the generalized Gorenstein dimension

Yuxian Geng (2013)

Czechoslovak Mathematical Journal

Let R be a left and right Noetherian ring and C a semidualizing R -bimodule. We introduce a transpose Tr c M of an R -module M with respect to C which unifies the Auslander transpose and Huang’s transpose, see Z. Y. Huang, On a generalization of the Auslander-Bridger transpose, Comm. Algebra 27 (1999), 5791–5812, in the two-sided Noetherian setting, and use Tr c M to develop further the generalized Gorenstein dimension with respect to C . Especially, we generalize the Auslander-Bridger formula to the generalized...

A procedure to compute prime filtration

Asia Rauf (2010)

Open Mathematics

Let K be a field, S = K[x 1, … x n] be a polynomial ring in n variables over K and I ⊂ S be an ideal. We give a procedure to compute a prime filtration of S/I. We proceed as in the classical case by constructing an ascending chain of ideals of S starting from I and ending at S. The procedure of this paper is developed and has been implemented in the computer algebra system Singular.

Absolutely S-domains and pseudo-polynomial rings

Noomen Jarboui, Ihsen Yengui (2002)

Colloquium Mathematicae

A domain R is called an absolutely S-domain (for short, AS-domain) if each domain T such that R ⊆ T ⊆ qf(R) is an S-domain. We show that R is an AS-domain if and only if for each valuation overring V of R and each height one prime ideal q of V, the extension R/(q ∩ R) ⊆ V/q is algebraic. A Noetherian domain R is an AS-domain if and only if dim (R) ≤ 1. In Section 2, we study a class of R-subalgebras of R[X] which share many spectral properties with the polynomial ring R[X] and which we call pseudo-polynomial...

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