On Graded Second and Coprimary Modules and Graded Secondary Representations

Ceken S., ALKAN M.

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, cilt.38, sa.4, ss.1317-1330, 2015 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 4
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1007/s40840-014-0097-6
  • Dergi Adı: BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1317-1330
  • Anahtar Kelimeler: Graded second module, Graded coprimary module, Graded prime submodule, Graded primary ideal, Graded secondary module, PRIME
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.

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