ABELIAN GROUPS WITH A p(2)-BOUNDED SUBGROUP, REVISITED

作者：Petroro Carla^*; Schmidmeier Markus

来源：Journal of Algebra and Its Applications, 2011, 10(3): 377-389.

DOI：10.1142/S0219498811004823

• Subgroups of abelian groups
• uniserial rings
• poset representations

Let Lambda be a commutative local uniserial ring of length n, p be a generator of the maximal ideal, and k be the radical factor field. The pairs (B, Lambda) where B is a finitely generated Lambda-module and A subset of B a submodule of B such that p(m) A = 0 form the objects in the category S-m(Lambda). We show that in case m = 2 the categories S-m(Lambda) are in fact quite similar to each other: If also Delta is a commutative local uniserial ring of length n and with radical factor field k, then the categories S-2(Lambda)/N-Lambda and S-2(Delta)/N-Delta are equivalent for certain nilpotent categorical ideals N-Lambda and N-Delta. As an application, we recover the known classification of all pairs (B, A) where B is a finitely generated abelian group and A subset of B a subgroup of B which is p(2)-bounded for a given prime number p.

• 出版日期2011-6