Computing Hilbert-Kunz functions of 1-dimensional graded rings.
Kreuzer, Martin (2007)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Kreuzer, Martin (2007)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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The space of maximal ideals is studied on semiprimitive rings and reduced rings, and the relation between topological properties of Max(R) and algebric properties of the ring R are investigated. The socle of semiprimitive rings is characterized homologically, and it is shown that the socle is a direct sum of its localizations with respect to isolated maximal ideals. We observe that the Goldie dimension of a semiprimitive ring R is equal to the Suslin number of Max(R).
Verma, J.K. (2002)
Beiträge zur Algebra und Geometrie
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Chaopraknoi, Sureeporn, Savettaseranee, Knograt, Lertwichitsilp, Patcharee (2005)
General Mathematics
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Jarnicki, Witold, O'Carroll, Liam, Winiarski, Tadeusz (2001)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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Solčan, Š. (2000)
Acta Mathematica Universitatis Comenianae. New Series
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A. Caruth (1993)
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Y. Tiraş (1993)
Colloquium Mathematicae
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The important ideas of reduction and integral closure of an ideal in a commutative Noetherian ring A (with identity) were introduced by Northcott and Rees [4]; a brief and direct approach to their theory is given in [6, (1.1)]. We begin by briefly summarizing some of the main aspects.
D'Cruz, Clare (2006)
Beiträge zur Algebra und Geometrie
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Herzog, Jürgen, Restuccia, Gaetana, Rinaldo, Giancarlo (2006)
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Oneto, Anna, Zatini, Elsa (2005)
Beiträge zur Algebra und Geometrie
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Farzad Fatehi, Mohammad Reza Molaei (2014)
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The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups. We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. We prove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deduce a characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if R is a Noetherian graded ring, then each summand of it is also a Noetherian...