ESSENTIAL SUBMODULES WITH RESPECT TO AN ARBITRARY SUBMODULE

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SAFAEEYAN S.; SABOORI SHIRAZI N.

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Paper Information

Journal: JOURNAL OF MATHEMATICAL EXTENSION Year:2013 | Volume:7 | Issue:3 (S.N. 18) Page(s): 15-27

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Information Journal Paper

Title

ESSENTIAL SUBMODULES WITH RESPECT TO AN ARBITRARY SUBMODULE

Author(s)

SAFAEEYAN S. | SABOORI SHIRAZI N. | Issue Writer Certificate

Keywords

ESSENTIAL SUBMODULES

S-ESSENTIAL SUBMODULES

SOCLE OF A MODULE

Abstract

The concept of ESSENTIAL SUBMODULES is a well known concept. In this paper we try to replace an arbitrary submodule of M, say T, instead of 0 in the definition of ESSENTIAL SUBMODULES. By this, ESSENTIAL SUBMODULES are precisely {0}-ESSENTIAL SUBMODULES. For a submodule K of right R-module M, we have Íess M if and only if (K: m) is annr (m)-essential right ideal of R, for each mÎM \ {0}. Among other things, this generalization of ESSENTIAL SUBMODULES gives a necessary and sufficient condition for M/T being finitely co-generated.

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APA: Copy

SAFAEEYAN, S., & SABOORI SHIRAZI, N.. (2013). ESSENTIAL SUBMODULES WITH RESPECT TO AN ARBITRARY SUBMODULE. JOURNAL OF MATHEMATICAL EXTENSION, 7(3 (S.N. 18)), 15-27. SID. https://sid.ir/paper/638681/en

Vancouver: Copy

SAFAEEYAN S., SABOORI SHIRAZI N.. ESSENTIAL SUBMODULES WITH RESPECT TO AN ARBITRARY SUBMODULE. JOURNAL OF MATHEMATICAL EXTENSION[Internet]. 2013;7(3 (S.N. 18)):15-27. Available from: https://sid.ir/paper/638681/en

IEEE: Copy

S. SAFAEEYAN, and N. SABOORI SHIRAZI, “ESSENTIAL SUBMODULES WITH RESPECT TO AN ARBITRARY SUBMODULE,” JOURNAL OF MATHEMATICAL EXTENSION, vol. 7, no. 3 (S.N. 18), pp. 15–27, 2013, [Online]. Available: https://sid.ir/paper/638681/en

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