12 citations · 19 across the 7 of their papers we have counts for
7 papers
Canonical Degrees of Cohen-Macaulay Rings and Modules: a Survey
J. P. Brennan, L. Ghezzi, J. Hong +2
The aim of this survey is to discuss invariants of Cohen-Macaulay local rings that admit a canonical module. Attached to each such ring R with a canonical ideal C, there are intege…
Linkage and Intermediate C-Gorenstein Dimensions
Joseph P. Brennan, Alexander York
This paper brings together two theories in algebra that have had been extensively developed in recent years. First is the study of various homological dimensions and what informati…
An Extension of a Theorem of Frobenius and Stickelberger to Modules of Projective Dimension One over a Factorial Domain
Joseph P. Brennan, Alexander York
Let be a commutative ring. A quasi-Gorenstein -module is an -module such that the grade of the module and the projective dimension of the module are equal and the canonic…
Chermak-Delgado Lattice Extension Theorems
Lijian An, Joseph Brennan, Haipeng Qu +1
In a finite group G with subgroup H, the Chermak-Delgado measure of H (in G) is defined as the product of the order of H with the order of the centralizer of H. The Chermak-Delgado…
Noether normalizations, reductions of ideals, and matroids
Joseph P. Brennan, Neil Epstein
We show that given a finitely generated standard-graded algebra of dimension over an infinite field, its graded Noether normalizations obey a certain kind of `generic exchange'…
Efficient quantum processing of ideals in finite rings
Pawel M. Wocjan, Stephen P. Jordan, Hamed Ahmadi +1
Suppose we are given black-box access to a finite ring R, and a list of generators for an ideal I in R. We show how to find an additive basis representation for I in poly(log |R|)…
Duality, a-invariants and canonical modules of rings arising from linear optimization problems
Joseph P. Brennan, Luis A. Dupont, Rafael H. Villarreal
The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial…