In the early 1900~ 4, Wedderburn classified the isomorphisms between matrix rings over
division rings in the following manner. Let@: End,,(V,)+ EndD2 (VZ) be a ring isomorphism …

Given modules M and P, we introduce in section 2 the concept of an (M, P)-injective module.
This concept contains many versions of injectivity known in the literature, such as principal …

ABSTRACT A module M is called strongly FP-injective if Ext i (P, M)= 0 for any finitely
presented module P and all i≥ 1.(Pre) envelopes and (pre) covers by strongly FP-injective …

If R is a Noetherian ring and I is an ideal of R, then the Rees ring R (J)= R@ I@- I”@-, L
nothing but the graded ring associateId to the I-aclic filtration of R. The use of such rings in …

Let R be a discrete valuation ring with field of fractions F and let C be a central simple F-
algebra. There exists a well-developed theory of the R-orders in C, that is those R …

Utilizing a matrix representation of semiperfect rings by a family of bimodules over local
rings, we describe the structure of generalized quasi-Frobenius rings in two steps: a cyclic …

In this note, we characterize quasi-Frobenius rings by a weakened form of the usual
condition, that every ideal is an annihilator ideal. We then apply this result to pure rings in …

It is shown that for any local strongly-regular ring there exists natural number so that if is any
finitely generated maximal Cohen–Macaulay module, then the pushforward of under the th …

arXiv:1312.1250v1 [math.AC] 4 Dec 2013 Page 1 arXiv:1312.1250v1 [math.AC] 4 Dec 2013
FIP AND FCP PRODUCTS OF RING MORPHISMS GABRIEL PICAVET AND MARTINE …

Call a ring Λ (left) absolutely torsion− f 7⋅ ee (ATF) if for every finite kernel functor σ (ie, a
topologizing filter of nonzero left ideals), σ (Λ)= 0. Since a commutative ring is ATF iff it is an …