A CRITERION FOR GORENSTEIN ALGEBRAS TO BE REGULAR

作者：Mao, X. -F.^*; Wu, Q. -S.

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139(5): 1543-1552.

DOI：10.1090/S0002-9939-2010-10586-5

• Connected graded algebra
• Gorenstein algebra
• AS-Gorenstein algebra
• AS-regular algebra

In this paper we give a criterion for a left Gorenstein algebra to be AS-regular. Let A be a left Gorenstein algebra such that the trivial module A(k) admits a finitely generated minimal free resolution. Then A is AS-regular if and only if its left Gorenstein index is equal to -inf{i| Ext(A)(depthAA) (k,k)(i) not equal 0}. Furthermore, A is Koszul AS-regular if and only if its left Gorenstein index is depth (A)A = -inf{i| Ext(A)(depthAA) (k,k)(i) not equal 0}.
As applications, we prove that the category of AS-regular algebras is a tensor category and that a left Noetherian p-Koszul, left Gorenstein algebra is AS-regular if and only if it is p-standard. This generalizes a result of Dong and the second author.

• 出版日期2011-5
• 单位上海大学; 复旦大学