Divisor sequences of atoms in Krull monoids
TL;DR: In this article , it was shown that positive integer sequences of positive integers can be realized as divisor sequences of irreducible elements in Krull monoids, which gives a means for studying nonunique direct-sum decompositions of modules over local Noetherian rings for which the Krull-Remak-Schmidt property fails.
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Abstract: The divisor sequence of an irreducible element (atom) a of a reduced monoid H is the sequence (sn)n∈ℕ where, for each positive integer n, sn denotes the number of distinct irreducible divisors of an. We investigate which sequences of positive integers can be realized as divisor sequences of irreducible elements in Krull monoids. In particular, this gives a means for studying nonunique direct-sum decompositions of modules over local Noetherian rings for which the Krull–Remak–Schmidt property fails.
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Citations
On Algebraic Properties of Power Monoids of Numerical Monoids
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TL;DR: This study investigates algebraic properties of power monoids, specifically prime spectrum and irreducibility, in numerical monoids, complementing existing literature on their arithmetic.
References
•Book
Cohen-Macaulay rings
Winfried Bruns,H. Jürgen Herzog +1 more
- 01 Jan 1993
TL;DR: In this article, the authors present a self-contained introduction to the homological and combinatorial aspects of the theory of Cohen-Macaulay rings, Gorenstein rings, local cohomology, and canonical modules.
3.3K
•Book
Noetherian Semigroup Algebras
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- 21 Feb 2007
TL;DR: In this paper, the authors present a characterization of the structure of semigroups of skew type and the Gelfand-Kirillov dimension of a monoid of I-type.
102
Non-commutative krull monoids: a divisor theoretic approach and their arithmetic
TL;DR: In this paper, the authors study the structure of Krull monoids, both with ideal theoretic and with divisor theoretic methods, and provide arithmetical finiteness results in case of normalizing Krull Monoid with finite Davenport constant.