Families of generalized Cohen-Macaulay and filter rings

摘要

Let R be a commutative ring with unity, a,b is an element of R, and I an ideal of R. Define R(I)(a,b) to be R+/(I-2(t(2)+ at + b)), a quotient of the Rees algebra. In this paper, we investigate when the rings in the family are generalized Cohen-Macaulay or filter rings and show that these properties are independent of the choice of a and b.