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1,301
Coinduction for semigroupgraded rings
 Comm. Algebra 1999
"... We describe the gradedsimple modules over a semigroupgraded ring in terms of the simple modules over various component subrings. Our method utilizes the coinduction functors Coindx. Let G be a group with identity e, let R be a Ggraded ring, and let M be any Ggraded left Rmodule. For each g ∈ G, ..."
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Cited by 2 (1 self)
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We describe the gradedsimple modules over a semigroupgraded ring in terms of the simple modules over various component subrings. Our method utilizes the coinduction functors Coindx. Let G be a group with identity e, let R be a Ggraded ring, and let M be any Ggraded left Rmodule. For each g ∈ G
Dimensions of Crystalline Graded Rings
, 2009
"... The global dimension of a ring governs many useful abilities. For example, it is semisimple if the global dimension is 0, hereditary if it is 1 and so on. We will calculate the global dimension of a Crystalline Graded Ring, as de ned in the paper by E. Nauwelaerts and F. Van Oystaeyen, [10]. We wil ..."
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The global dimension of a ring governs many useful abilities. For example, it is semisimple if the global dimension is 0, hereditary if it is 1 and so on. We will calculate the global dimension of a Crystalline Graded Ring, as de ned in the paper by E. Nauwelaerts and F. Van Oystaeyen, [10]. We
The Center of Crystalline Graded Rings
, 2009
"... In the rst section of the paper, we will give some basic de nitions and properties about Crystalline Graded Rings. In the following section we will provide a general description of the center. Afterwards, the case where the grading group is Abelian nite will be handled. The center will have some pro ..."
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Cited by 1 (0 self)
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In the rst section of the paper, we will give some basic de nitions and properties about Crystalline Graded Rings. In the following section we will provide a general description of the center. Afterwards, the case where the grading group is Abelian nite will be handled. The center will have some
Approximate Roots in Graded Rings
, 2005
"... An approximate root of an univariate polynomial over a graded ring A is an element in A for which the evaluated polynomial vanishes up to a prescribed order. We give an algorithm for deciding existence of approximate roots and computing essentially all of them. Based on this algorithm we also sugges ..."
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Cited by 2 (2 self)
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An approximate root of an univariate polynomial over a graded ring A is an element in A for which the evaluated polynomial vanishes up to a prescribed order. We give an algorithm for deciding existence of approximate roots and computing essentially all of them. Based on this algorithm we also
Semisimple Strongly Graded Rings
, 2006
"... Let G be a finite group and R a strongly Ggraded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory answe ..."
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Let G be a finite group and R a strongly Ggraded ring. The question of when R is semisimple (meaning in this paper semisimple artinian) has been studied by several authors. The most classical result is Maschke’s Theorem for group rings. For crossed products over fields there is a satisfactory
Tight Closure In Graded Rings
 J. Math. Kyoto Univ
"... . This paper facilitates the computation of tight closure by giving giving upper and lower bounds on the degrees of elements that need to be checked for inclusion in the tight closure of certain homogeneous ideals in a graded ring. Differential operators are introduced to the study of tight closu ..."
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Cited by 14 (2 self)
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. This paper facilitates the computation of tight closure by giving giving upper and lower bounds on the degrees of elements that need to be checked for inclusion in the tight closure of certain homogeneous ideals in a graded ring. Differential operators are introduced to the study of tight
coefficients and the depths of associated graded ring
 J. London Math. Soc
, 1997
"... CohenMacaulay (abbr. CM) local ring R such that dimR/I = 0, what information about I and its associated graded ring can be obtained from the Hilbert function and Hilbert polynomial of I? By the Hilbert (or HilbertSamuel) function of I, we mean the function ..."
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Cited by 40 (1 self)
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CohenMacaulay (abbr. CM) local ring R such that dimR/I = 0, what information about I and its associated graded ring can be obtained from the Hilbert function and Hilbert polynomial of I? By the Hilbert (or HilbertSamuel) function of I, we mean the function
On Strongly Groupoid Graded Rings and the Corresponding Clifford Theorem∗
, 2005
"... Abstract. 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 cohom ..."
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Cited by 2 (0 self)
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Abstract. 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
Normal Ideals of Graded Rings
 Comm. Algebra 2000
"... Abstract. For a graded domain R = k[X0,...,Xm]/J over an arbitrary domain k, it is shown that the ideal generated by elements of degree ≥ mA, where A is the least common multiple of the weights of the Xi, is a normal ideal. 1. ..."
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Abstract. For a graded domain R = k[X0,...,Xm]/J over an arbitrary domain k, it is shown that the ideal generated by elements of degree ≥ mA, where A is the least common multiple of the weights of the Xi, is a normal ideal. 1.
Blocks of Fully Graded Rings
, 1997
"... this paper was precipitated by a curious observation relating the blocks of a Gring T, for some finite group G, to the blocks of the fixed subring T ..."
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this paper was precipitated by a curious observation relating the blocks of a Gring T, for some finite group G, to the blocks of the fixed subring T
Results 1  10
of
1,301