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...
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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
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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...
متن کاملCurves arising from endomorphism rings of Kronecker modules
In this note, we prove that the endomorphism ring of a Kronecker module attached to a power series α ∈ k[[X]] is minimally generated by three generators, unless its degree d is less than 3. We prove this via the theory of algebraic curves, by proving that none of the affine curves arising from these endomorphism rings are planar for d ≥ 3, but can always be embedded in A3.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1971
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1971-0274511-2