LOCAL DIMENSION AND DIRECT SUM OF CYCLIC MODULES

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GHORBANI ATEFEH; Naji Esfahani Mahdieh

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Seminar Paper

Paper Information

Seminar: ANNUAL IRANIAN MATHEMATICS CONFERENCE
Year:2015 | Issue:46

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Title

LOCAL DIMENSION AND DIRECT SUM OF CYCLIC MODULES

Author(s)

GHORBANI ATEFEH | Naji Esfahani Mahdieh | Issue Writer Certificate

Keywords

LOCAL DIMENSION

CYCLIC MODULES

PRINCIPAL IDEAL RING

ARTINIAN RING

Abstract

IN THIS PAPER WE STUDY RINGS WITH LOCAL DIMENSION WHICH CERTAIN OF IDEALS ARE DIRECT SUM OF CYCLIC MODULES. IT IS SHOWN THAT FOR A COMMUTATIVE RING R WITH LOCAL DIMENSION W EVERY IDEAL IS DIRECT SUM OF CYCLIC MODULES IF AND ONLY IF R IS A PRINCIPAL IDEAL DOMAIN. WE SHOW THAT FOR A NON-LOCAL RING R WITH FINITE LOCAL DIMENSION IF EVERY IDEAL OF R IS A DIRECT SUM CYCLIC RIGHT R-MODULES, THEN R IS RIGHT ARTINIAN.

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APA: Copy

GHORBANI, ATEFEH, & Naji Esfahani, Mahdieh. (2015). LOCAL DIMENSION AND DIRECT SUM OF CYCLIC MODULES. ANNUAL IRANIAN MATHEMATICS CONFERENCE. SID. https://sid.ir/paper/921006/en

Vancouver: Copy

GHORBANI ATEFEH, Naji Esfahani Mahdieh. LOCAL DIMENSION AND DIRECT SUM OF CYCLIC MODULES. 2015. Available from: https://sid.ir/paper/921006/en

IEEE: Copy

ATEFEH GHORBANI, and Mahdieh Naji Esfahani, “LOCAL DIMENSION AND DIRECT SUM OF CYCLIC MODULES,” presented at the ANNUAL IRANIAN MATHEMATICS CONFERENCE. 2015, [Online]. Available: https://sid.ir/paper/921006/en

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