… Then, the stable value [Sn+q,S n] for n sufficiently large is known as the q-th stable
homotopy group of spheres, πq. The cohomology of A with k-coefficients, ExtA(k, k) = {Ext …

… 0 B ) are studied via modules over diagonal “small rings” A and B. However, we use model
… modules to characterize the stable categories GP(A), GP(B) of Gorenstein projective modules …

… Abstract: Let R be a commutative ring, C a semidualizing R-module and X a class of R-modules.
The notion of XG C -projective complexes is introduced, and it is shown that a complex …

… module M 1 and left B-module M 2 . Moreover, we establish a relationship of left global
Gorenstein AC-projective dimensions of ring … -projective dimension of the ring and Gorenstein AC-…

… coincide for any ring. We investigate the … stable categories with respect to Ding modules,
and characterize Gorenstein (regular) rings and the finiteness of left global dimension of rings in …

… Abstract: Let be a formal triangular matrix ring, where A and B are rings and U is a (B, A)-bimodule.
We prove that, if BU has finite flat dimension, and UA has finite flat or injective …

… injective module and Frobenius bimodules. Let R and S be associative rings with an identity…
We proved that (1) R op -module X is Y- Gorenstein injective module if and only if Hom Rop (…

… Bott found the important periodicity of stable homotopic groups of classical groups. J. Milnor
introduced surgery theory while S. Smale proved the h-cobordism theorem, which implies …

… Abstract: Let R be a ring and n≥1 be an integer. As a generalization of Gorenstein FP-projective
modules, Gorenstein FP n -projective modules have been introduced and investigated …