ON 2-ABSORBING PRIMARY SUBMODULES OF MODULES OVER COMMUTATIVE RINGS

Mostafanasab H., Yetkin E., TEKİR Ü., Darani A. Y.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.24, sa.1, ss.335-351, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1515/auom-2016-0020
  • Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.335-351
  • Anahtar Kelimeler: Multiplication module, Primary submodule, Prime submodule, 2-absorbing submodule, n-absorbing submodule, IDEALS, RADICALS
  • Marmara Üniversitesi Adresli: Evet

Özet

All rings are commutative with 1 not equal 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2 -absorbing primary submodules generalizing 2 -absorbing primary ideals of rings. Let M be an R -module. A proper submodule N of an R -module M is called a 2 -absorbing primary submodule of M if whenever a, b is an element of R and m is an element of M and abm is an element of N, then am is an element of M-rad(N) or bm is an element of M-rad(N) or ab is an element of (N :(R) M). It is shown that a proper submodule N of M is a 2 -absorbing primary submodule if and only if whenever I-1 I-2 K subset of N for some ideals I-1,I-2 of R and some submodule K of M, then I-1,I-2 subset of (N :(R) M) or I-1 K subset of M-rad(N) or I2K subset of M-rad(N). We prove that for a submodule N of an R -module M if M-rad(N) is a prime submodule of M, then N is a 2 -absorbing primary submodule of M. If N is a 2 -absorbing primary submodule of a finitely generated multiplication R -module M, then (N :(R) M) is a 2 -absorbing primary ideal of R and M-rad(N) is a 2 -absorbing submodule of M.