منابع مشابه
Commutative Nil Clean Group Rings
In [5] and [6], a nil clean ring was defined as a ring for which every element is the sum of a nilpotent and an idempotent. In this short article we characterize nil clean commutative group rings.
متن کاملStrongly nil-clean corner rings
We show that if $R$ is a ring with an arbitrary idempotent $e$ such that $eRe$ and $(1-e)R(1-e)$ are both strongly nil-clean rings, then $R/J(R)$ is nil-clean. In particular, under certain additional circumstances, $R$ is also nil-clean. These results somewhat improves on achievements due to Diesl in J. Algebra (2013) and to Koc{s}an-Wang-Zhou in J. Pure Appl. Algebra (2016). ...
متن کاملOn primitive ideals in polynomial rings over nil rings
Let R be a nil ring. We prove that primitive ideals in the polynomial ring R[x] in one indeterminate over R are of the form I [x] for some ideals I of R. All considered rings are associative but not necessarily have identities. Köthe’s conjecture states that a ring without nil ideals has no one-sided nil ideals. It is equivalent [4] to the assertion that polynomial rings over nil rings are Jaco...
متن کاملOn Regular Group Rings
Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...
متن کاملLocally Compact Topologically Nil and Monocompact PI-rings
In this note we shall investigate a topological version of the problem of Kurosh: “Is any algebraic algebra locally finite?” Kaplansky’s theorem concerning the local nilpotence of nil PI-algebras is well-known. We will prove a generalization of Kaplansky’s theorem to the class of locally compact rings. We use in the proof a theorem of A. I. Shirshov [8] concerning the height of a finitely gener...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 1976
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-92-1-17-23