On Weakly Regular Rings and SSF-rings | Zendy

Raida Mahmood | Zendy

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On Weakly Regular Rings and SSF-rings

Author(s) -

Raida Mahmood

Publication year - 2006

Publication title -

maǧallaẗ al-rāfidayn li-ʿulūm al-ḥāsibāt wa-al-riyāḍiyyāẗ/al-rafidain journal for computer sciences and mathematics

Language(s) - English

Resource type - Journals

eISSN - 2311-7990

pISSN - 1815-4816

DOI - 10.33899/csmj.2006.164035

Subject(s) - mathematics , von neumann regular ring , ring (chemistry) , simple (philosophy) , regular ring , bounded function , center (category theory) , simple ring , combinatorics , simple module , local ring , pure mathematics , principal ideal ring , discrete mathematics , mathematical analysis , commutative ring , crystallography , chemistry , organic chemistry , philosophy , epistemology , commutative property

ABSRACT In this work we consider weakly regular rings whose simple singular right R-Modules are flat. We also consider the condition (*): R satisfies L(a)r(a) for any aR. We prove that if R satisfies(*) and whose simple singular right R-module are flat, then Z (R) the center of R is a von Neunann regular ring. We also show that a ring R either satisfies (*) or a strongly right bounded ring in which every simple singular right R-module is flat, then R is reduced weakly regular rings.

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