On Graded Second and Coprimary Modules and Graded Secondary Representations


Ceken S., ALKAN M.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, vol.38, no.4, pp.1317-1330, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 4
  • Publication Date: 2015
  • Doi Number: 10.1007/s40840-014-0097-6
  • Journal Name: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1317-1330
  • Keywords: Graded second module, Graded coprimary module, Graded prime submodule, Graded primary ideal, Graded secondary module, PRIME
  • Akdeniz University Affiliated: Yes

Abstract

In this paper we introduce and study the concepts of graded second (grsecond)
and graded coprimary (gr-coprimary) modules which are different from second
and coprimary modules over arbitrary-graded rings. We list some properties
and characterizations of gr-second and gr-coprimary modules and also study graded
prime submodules of modules with gr-coprimary decompositions. We also deal with
graded secondary representations for graded injective modules over commutativegraded
rings. By using the concept of σ-suspension (σ )M of a graded module M, we
prove that a graded injective module over a commutative graded Noetherian ring has
a graded secondary representation.
Keywords Graded second module · Graded coprimary module · Graded prime
submodule · Graded primary ideal · Graded secondary module
Mathematics Subject Classification 16W50 · 16U30 · 16N60 · 13A02 · 13C11

In this paper we introduce and study the concepts of graded second (gr-second) and graded coprimary (gr-coprimary) modules which are different from second and coprimary modules over arbitrary-graded rings. We list some properties and characterizations of gr-second and gr-coprimary modules and also study graded prime submodules of modules with gr-coprimary decompositions. We also deal with graded secondary representations for graded injective modules over commutative-graded rings. By using the concept of sigma-suspension (sigma)M of a graded module M, we prove that a graded injective module over a commutative graded Noetherian ring has a graded secondary representation.