منابع مشابه
Endomorphism Rings of Protective Modules
The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose endomorphism rings are (von Neumann) regular, local semiperfect, or left perfect. Call a projective module regular if every cyclic submodule is a direct summand. Thus a ring is a regular module if it is...
متن کاملEndomorphism Rings of Modules over Prime Rings
Endomorphism rings of modules appear as the center of a ring, as the fix ring of a ring with group action or as the subring of constants of a derivation. This note discusses the question whether certain ∗-prime modules have a prime endomorphism ring. Several conditions are presented that guarantee the primeness of the endomorphism ring. The contours of a possible example of a ∗-prime module who...
متن کاملModules with Dedekind Finite Endomorphism Rings
This article is a survey of modules whose endomorphism rings are Dedekind finite, Hopfian or co-Hopfian. We summarise the properties of such modules and present unified proofs of known results and generalisations to new structure theorems. MSC 2010. 16S50, 16D80.
متن کاملOn Endomorphism Rings and Dimensions of Local Cohomology Modules
Let (R, m) denote an n-dimensional complete local Gorenstein ring. For an ideal I of R let H I(R), i ∈ Z, denote the local cohomology modules of R with respect to I. If H i I(R) = 0 for all i 6= c = height I, then the endomorphism ring of H I (R) is isomorphic to R (cf. [5] and [4]). Here we prove that this is true if and only if H I(R) = 0, i = n, n − 1 provided c ≥ 2 and R/I has an isolated s...
متن کاملDirect-sum decompositions of modules with semilocal endomorphism rings
Let R be a ring and C a class of right R-modules closed under finite direct sums. If we suppose that C has a set of representatives, that is, a set V(C) ⊆ C such that every M ∈ C is isomorphic to a unique element [M ] ∈ V(C), then we can view V(C) as a monoid, with the monoid operation [M1] + [M2] = [M1 ⊕M2]. Recent developments in the theory of commutative monoids (e.g., [4], [15]) suggest tha...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2002
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181070042