Rings close to strongly von Neumann regular
نویسندگان
چکیده
منابع مشابه
Relative Regular Modules. Applications to von Neumann Regular Rings
We use the concept of a regular object with respect to another object in an arbitrary category, defined in [3], in order to obtain the transfer of regularity in the sense of Zelmanowitz between the categories R−mod and S−mod, when S is an excellent extension of the ring R. Consequently, we obtain a result of [5]: if S is an excellent extension of the ring R, then S is von Neumann regular ring i...
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All rings R considered are commutative and have an identity element. Contessa called R a VNL-ring if a or 1 a has a Von Neumann inverse whenever a 2 R. Sample results: Every prime ideal of a VNL-ring is contained in a unique maximal ideal. Local and Von Neumann regular rings are VNL and if the product of two rings is VNL, then both are Von Neumann regular, or one is Von Neumann regular and the ...
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The aim of this paper is to prove that, if R is a commutative regular ring in which 2 is a unit, then the reduced theory of quadratic forms with invertible coefficients in R, modulo a proper preorder T , satisfies Marshall’s signature conjecture and Milnor’s Witt ring conjecture (for precise statements, see Section 1 below). For that purpose we use the theory of special groups (abbreviated SG),...
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All rings considered are associative with identity and all occurring modules are unital right modules. We denote by Mod R the category of all R-modules. The spectrum of a ring R is known to be the “set” of isomorphism classes of indecomposable injective right R-modules. When R is right-Noetherian the spectrum describes all injective Rmodules, since each injective module is a direct sum of indec...
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ژورنال
عنوان ژورنال: Journal of Nepal Mathematical Society
سال: 2019
ISSN: 2616-0161,2616-0153
DOI: 10.3126/jnms.v2i1.33013