Displaying similar documents to “On a theorem of F. S. Macaulay on colon ideals.”

Rings Graded By a Generalized Group

Farzad Fatehi, Mohammad Reza Molaei (2014)

Topological Algebra and its Applications

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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...

Representation theory of two-dimensionalbrauer graph rings

Wolfgang Rump (2000)

Colloquium Mathematicae

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We consider a class of two-dimensional non-commutative Cohen-Macaulay rings to which a Brauer graph, that is, a finite graph endowed with a cyclic ordering of edges at any vertex, can be associated in a natural way. Some orders Λ over a two-dimensional regular local ring are of this type. They arise, e.g., as certain blocks of Hecke algebras over the completion of ℤ [ q , q - 1 ] at (p,q-1) for some rational prime p . For such orders Λ, a class of indecomposable maximal Cohen-Macaulay modules (see...

Integral closures of ideals in the Rees ring

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.