Multiplication modules and homogeneous idealization

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4 Citations (Scopus)

Abstract

All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M. Homogeneous ideals of R (M) have the form I(+N where I is an ideal of R, N a submodule of M and IM ⊆ N. The purpose of this paper is to investigate how properties of a homogeneous ideal I(+)N of R (M) are related to those of I and N. We show that if M is a multiplication R-module and I(-))N is a meet principal (join principal) homogeneous ideal of R (M) then these properties can be transferred to I and N. We give some conditions under which the converse is true. We also show that I(-)N is large (small) if and only if N is large in M (I is a small ideal of R).

Original languageEnglish
Pages (from-to)249-270
Number of pages22
JournalBeitrage zur Algebra und Geometrie
Volume47
Issue number1
Publication statusPublished - 2006

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Keywords

  • Idealization
  • Join principal submodule
  • Large submodule
  • Meet principal module
  • Multiplication module
  • Small submodule

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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