Results 261 to 270 of about 11,543 (300)

Graded π-rings

Canadian Journal of Mathematics, 1979
All rings considered will be commutative with identity. By a graded ring we will mean a ring graded by the non-negative integers.A ring R is called a π-ring if every principal ideal of R is a product of prime ideals. A π-ring without divisors of zero is called a π-domain.
Anderson, D. D., Matijevic, J.
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Graded Semiartinian Rings: Graded Perfect Rings

Communications in Algebra, 2003
Abstract We study graded left semiartinian rings with finite support. It is shown that the semiartinian property is preserved when we pass to the smash product in the sense of Quinn. We apply these results to investigate left perfect graded rings.
C. Năstăsescu, L. Dăuş, B. Torrecillas   +2 more
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Bimodules in Group Graded Rings

Algebras and Representation Theory, 2017
In this article we introduce the notion of a controlled group graded ring. Let G be a group, with identity element e, and let R = aS center dot (gaG) R (g) be a unital G-graded ring.
Johan Öinert
exaly   +2 more sources

Commutativity and Ideals in Strongly Graded Rings

Acta Applicandae Mathematicae, 2009
In some recent papers by the first two authors it was shown that for any algebraic crossed product A, where A(0), the subring in the degree zero component of the grading, is a commutative ring, each non-zero two-sided ideal in A has a non-zero ...
Johan Öinert, Sergei Silvestrov, Silvestrov Sergei   +2 more
exaly   +2 more sources

Gabriel Dimension for Graded Rings

Applied Categorical Structures, 2006
Let \(G\) be a group with identity element \(e\), and let \(R=\bigoplus_{\sigma\in G}R_\sigma\) be a ring graded by \(G\), such that the grading has finite support. Using colocalization for Grothendieck categories with a family of projective generators, it is proved that if the category \(R_e\)-mod has Gabriel dimension, then so does the category \(R\)-
M. J. Asensio, Constantin Nastasescu, Blas Torrecillas   +2 more
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Graded radicals of graded rings

Acta Mathematica Hungarica, 1991
Let \(\lambda\) be a radical property in the category of associative rings and \(G\) a group. By means of the smash product a corresponding radical property \(\lambda_{\text{ref}}\) is defined in the category of associative \(G\)-graded rings. The authors describe these radicals and the relationship with the corresponding classical graded radicals for ...
Beattie, M., Stewart, P.
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Graded Quotient Rings

Journal of Mathematical Sciences, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Graded varieties of graded rings

Acta Mathematica Hungarica, 1995
\(G\)-graded rings with an identity are considered where \(G\) is a finite group. First the concept of a graded variety is introduced and the graded version of Birkhoff's Theorem is proved. A proper subclass \({\mathcal V}\) of all \(G\)-graded rings is a graded radical graded semisimple class if and only if \({\mathcal V} \subseteq {\mathcal D}^g ...
Sands, A. D., Yahya, H.
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Quotient rings of graded associative rings. I

Journal of Mathematical Sciences, 2012
The paper under review is a survey concerning graded quotient rings of associative rings graded by groups. Some new results are also included. The paper is structured in ten sections as follows: 1. Basic definitions and properties, 2. Graded analogs of classical notions, 3. Graded rational extensions and rings of quotients, 4.
Balaba, I. N., Kanunnikov, A. L., Mikhalev, A. V.   +2 more
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Morita duality and graded rings

Communications in Algebra, 1991
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MENINI, Claudia, A. del RIO MATEOS
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