The Jacobson radical of rings with nilpotent homogeneous elements
نویسندگان
چکیده
منابع مشابه
Nilpotent Elements in Skew Polynomial Rings
Letbe a ring with an endomorphism and an -derivationAntoine studied the structure of the set of nilpotent elements in Armendariz rings and introduced nil-Armendariz rings. In this paper we introduce and investigate the notion of nil--compatible rings. The class of nil--compatible rings are extended through various ring extensions and many classes of nil--compatible rings are constructed. We al...
متن کاملOn the Nilpotency of the Jacobson Radical of Semigroup Rings
Munn [11] proved that the Jacobson radical of a commutative semigroup ring is nil provided that the radical of the coefficient ring is nil. This was generalized, for semigroup algebras satisfying polynomial identities, by Okniński [14] (cf. [15, Chapter 21]), and for semigroup rings of commutative semigroups with Noetherian rings of coefficients, by Jespers [4]. It would be interesting to obtai...
متن کاملThe Upper Nilradical and Jacobson Radical of Semigroup Graded Rings
Given a semigroup S, we prove that if the upper nilradical Nil∗(R) is homogeneous whenever R is an S-graded ring, then the semigroup S must be cancelative and torsion-free. In case S is commutative the converse is true. Analogs of these results are established for other radicals and ideals. We also describe a large class of semigroups S with the property that whenever R is a Jacobson radical ri...
متن کاملOn the Jacobson radical of strongly group graded rings
For any non-torsion group G with identity e, we construct a strongly G-graded ring R such that the Jacobson radical J(Re) is locally nilpotent, but J(R) is not locally nilpotent. This answers a question posed by Puczy lowski.
متن کاملRings and Algebras the Jacobson Radical of a Semiring
The concept of the Jacobson radical of a ring is generalized to semirings. A semiring is a system consisting of a set S together with two binary operations, called addition and multiplication, which forms a semigroup relative to addition, a semigroup relative to multiplication, and the right and left distributive laws hold. The additive semigroup of S is assumed to be commutative. The right ide...
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: Bulletin of the London Mathematical Society
سال: 2008
ISSN: 0024-6093
DOI: 10.1112/blms/bdn086