Graded ring of a ring at an ideal

1982 ◽  
pp. 85-87
Author(s):  
Shreeram S. Abhyankar
Keyword(s):  
Graded Ring

scholarly journals The Spectrum of the Graded Ring of Differential Operators of a Scored Semigroup Algebra

2010 ◽  
Vol 38 (3) ◽  
pp. 829-847
Author(s):  
Mutsumi Saito
Keyword(s):  
Differential Operators ◽  
Semigroup Algebra ◽  
Graded Ring

An application of the method of orthogonal completeness in graded ring theory

2013 ◽  
Vol 52 (2) ◽  
pp. 98-104 ◽  
Author(s):  
A. L. Kanunnikov
Keyword(s):  
Ring Theory ◽  
Graded Ring ◽  
Orthogonal Completeness

scholarly journals A NOTE ON NIL AND JACOBSON RADICALS IN GRADED RINGS

2014 ◽  
Vol 13 (04) ◽  
pp. 1350121 ◽  
Author(s):  
AGATA SMOKTUNOWICZ
Keyword(s):  
Jacobson Radical ◽  
Analogous Result ◽  
Graded Rings ◽  
Radical Ring ◽  
Graded Ring ◽  
Nil Ring ◽  
Nil Radical

It was shown by Bergman that the Jacobson radical of a Z-graded ring is homogeneous. This paper shows that the analogous result holds for nil radicals, namely, that the nil radical of a Z-graded ring is homogeneous. It is obvious that a subring of a nil ring is nil, but generally a subring of a Jacobson radical ring need not be a Jacobson radical ring. In this paper, it is shown that every subring which is generated by homogeneous elements in a graded Jacobson radical ring is always a Jacobson radical ring. It is also observed that a ring whose all subrings are Jacobson radical rings is nil. Some new results on graded-nil rings are also obtained.

On Strongly Groupoid Graded Rings and the Corresponding Clifford Theorem

2006 ◽  
Vol 13 (02) ◽  
pp. 181-196 ◽  
Author(s):  
Gongxiang Liu ◽  
Fang Li
Keyword(s):  
Main Task ◽  
Graded Rings ◽  
Graded Ring ◽  
Matrix Rings ◽  
Definition Of

In this paper, we introduce the definition of groupoid graded rings. Group graded rings, (skew) groupoid rings, artinian semisimple rings, matrix rings and others can be regarded as special kinds of groupoid graded rings. Our main task is to classify strongly groupoid graded rings by cohomology of groupoids. Some classical results about group graded rings are generalized to groupoid graded rings. In particular, the Clifford Theorem for a strongly groupoid graded ring is given.

scholarly journals On the associated graded ring of an ideal

1982 ◽  
Vol 26 (1) ◽  
pp. 121-137 ◽  
Author(s):  
Craig Huneke
Keyword(s):  
Associated Graded Ring ◽  
Graded Ring

The spherical spectrum of a graded ring

1994 ◽  
Vol 52 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Gilbert Stengle ◽  
Hasan Yousef
Keyword(s):  
Graded Ring

Topics in graded ring theory

1979 ◽  
pp. 36-127
Author(s):  
C. Năstăsescu ◽  
F. Van Oystaeyen
Keyword(s):  
Ring Theory ◽  
Graded Ring

scholarly journals When Are Graded Rings Graded S-Noetherian Rings

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1532
Author(s):  
Dong Kyu Kim ◽  
Jung Wook Lim
Keyword(s):  
Noetherian Ring ◽  
Semigroup Ring ◽  
Noetherian Rings ◽  
Homogeneous Ideal ◽  
Commutative Monoid ◽  
Graded Rings ◽  
Graded Ring ◽  
Special Case

Let Γ be a commutative monoid, R=⨁α∈ΓRα a Γ-graded ring and S a multiplicative subset of R0. We define R to be a graded S-Noetherian ring if every homogeneous ideal of R is S-finite. In this paper, we characterize when the ring R is a graded S-Noetherian ring. As a special case, we also determine when the semigroup ring is a graded S-Noetherian ring. Finally, we give an example of a graded S-Noetherian ring which is not an S-Noetherian ring.

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