Gorenstein Projective Modules over Triangular Matrix Rings

Periodic modules over Gorenstein local rings

It is proved that the minimal free resolution of a module M over a Gorenstein local ring R is eventually periodic if, and only if, the class of M is torsion in a certain Z[t ±1 ]-module associated to R. This module, denoted J(R), is the free Z[t ±1 ]-module on the isomorphism classes of finitely generated R-modules modulo relations reminiscent of those defining the Grothendieck group of R. The ...

On Projective Modules over Semi-hereditary Rings

This theorem, already known for finitely generated projective modules[l, I, Proposition 6.1], has been recently proved for arbitrary projective modules over commutative semi-hereditary rings by I. Kaplansky [2], who raised the problem of extending it to the noncommutative case. We recall two results due to Kaplansky: Any projective module (over an arbitrary ring) is a direct sum of countably ge...

Differential Polynomial Rings of Triangular Matrix Rings

On Projective Geometry over Full Matrix Rings

1. K. L. Chung, Fluctuation of sums of independent random variables, Ann. of Math. vol. 51 (1950) pp. 697-706. 2. K. L. Chung and P. Erdos, Probability limit theorems assuming only the first moment. I, Memoirs of the American Mathematical Society, no. 6, pp. 13-19. 3.-, On the lower limit of sums of independent random variables, Ann. of Math. vol. 48 (1947) pp. 1003-1013. 4. K. L. Chung and W. ...

Strongly Gorenstein projective , injective and flat modules

Let R be a ring and n a fixed positive integer, we investigate the properties of n-strongly Gorenstein projective, injective and flat modules. Using the homological theory , we prove that the tensor product of an n-strongly Gorenstein projective (flat) right R -module and projective (flat) left R-module is also n-strongly Gorenstein projective (flat). Let R be a coherent ring ,we prove that the...