منابع مشابه
On Separable Abelian Extensions of Rings
Let R be a ring with I, G (= (1>x...Xm) a finite abelian automorphism group of R of order n where (i2 is cyclic of order n. for some integers n, hi, and m, and C the center of R whose automorphism group induced by G is isomorphic with G. Then an abelian extension Rtx 1,...,xm is defined as a generalization of cyclic extensions of rings, and RXl,...,Xm is an Azumaya algebra over K (= CG {c in C ...
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Let $R$ be an associative ring with identity. An element $x in R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if there exist $g in G$, $n in mathbb{Z}$ and $r in R$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). A ring $R$ is called $mathbb{Z}G$-regular (resp. strongly $mathbb{Z}G$-regular) if every element of $R$ is $mathbb{Z}G$-regular (resp. strongly $...
متن کاملCommutative Regular Rings without Prime Model Extensions
It is known that the theory K of commutative regular rings with identity has a model completion K . We show that there exists a countable model of K which has no prime extension to a model of K'. If K and K ate theories in a first order language L, then K is said to be a model completion of K if K extends K, every model of K can be embedded in a model of K , and for any model A of K and models ...
متن کاملExtensions of strongly alpha-reversible rings
We introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. We firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. We next argue about the strong$alpha$-reversibility of some kinds of extensions. A number ofproperties of this version are established. It is shown ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1980
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1980-0553363-8