Tor-prime and Strongly Tor-prime Submodules and Modules


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Authors

  • Payman Mahmood Hamaali Mathematics Department, College of Science, University of Sulaimani, Sulaimani
  • Rando Rasul Qadir Department of Mathematical Sciences, College of Basic Education, University of Sulaimani, Sulaimani

Abstract

The concepts of Tor-prime and Strongly Tor-prime submodules are introduced and investigated. A proper submodule N is called Tor- prime submodule (resp. Strongly prime), if rm∈N (resp. ((N+Rx):Tor(M))y⊆N), then m∈N or rTor(M)⊆N (resp. x∈N or y∈N). A proper submodule P is Tor-prime submodule of M if and only if P_S is a Tor-prime (res. Strongly Tor-prime) submodule in M_S, where S is a prime ideal of R. A finitely generated module M is Noetherian if and only if every Tor-prime submodule of M is finitely generated. Furthermore, the Cohen Theorem can be generalized for these new classes of submodules.

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Published

2023-09-17 — Updated on 2023-10-13

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How to Cite

Hamaali, P. M., & Qadir, R. R. (2023). Tor-prime and Strongly Tor-prime Submodules and Modules. Results in Nonlinear Analysis, 6(3), 82–89. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/205 (Original work published September 17, 2023)

Issue

Vol. 6 No. 3 (2023): volume 6 issue 3

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