A semigroup-theoretical view of direct-sum decompositions and associated combinatorial problems

作者：Baeth N R^*; Geroldinger A; Grynkiewicz D J; Smertnig D

来源：Journal of Algebra and Its Applications, 2015, 14(2): 1550016.

DOI：10.1142/S0219498815500164

• Krull monoids
• zero-sum sequences
• direct-sum decompositions
• indecomposable modules
• Prufer rings
• hereditary Noetherian prime rings

Let R be a ring and let C be a small class of right R-modules which is closed under finite direct sums, direct summands, and isomorphisms. Let V(C) denote a set of representatives of isomorphism classes in C and, for any module M in C, let [M] denote the unique element in V(C) isomorphic to M. Then V(C) is a reduced commutative semigroup with operation defined by [M] + [N] = [M circle plus N], and this semigroup carries all information about direct-sum decompositions of modules in C. This semigroup-theoretical point of view has been prevalent in the theory of direct-sum decompositions since it was shown that if End (R)(M) is semilocal for all M is an element of C, then V(C) is a Krull monoid. Suppose tha

• 出版日期2015-3