Polynomial rings over a commutative von Neumann regular ring
نویسندگان
چکیده
منابع مشابه
Commutative group rings with von Neumann regular total rings of quotients
Article history: Received 12 May 2011 Available online xxxx Communicated by Luchezar L. Avramov In memory of Miki Neumann
متن کاملCombining Local and Von Neumann Regular Rings
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 ...
متن کاملRelative 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...
متن کاملOn n-flat modules and n-Von Neumann regular rings
We show that each R-module is n-flat (resp., weakly n-flat) if and only if R is an (n,n− 1)-ring (resp., a weakly (n,n− 1)-ring). We also give a new characterization of n-von Neumann regular rings and a characterization of weak n-von Neumann regular rings for (CH)-rings and for local rings. Finally, we show that in a class of principal rings and a class of local Gaussian rings, a weak n-von Neu...
متن کاملMarshall’s and Milnor’s Conjectures for Preordered von Neumann Regular Rings
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),...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1975
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1975-0366907-4