On rings in which every ideal is weakly prime

Yasuyuki Hirano; Edward Poon; Hisaya Tsutsui

doi:10.4134/BKMS.2010.47.5.1077

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2010; 47(5): 1077-1087

Printed September 1, 2010

https://doi.org/10.4134/BKMS.2010.47.5.1077

On rings in which every ideal is weakly prime

Yasuyuki Hirano, Edward Poon, and Hisaya Tsutsui

Naruto University of Education, Embry-Riddle Aeronautical University, Embry-Riddle Aeronautical University

Abstract

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Abstract

Anderson-Smith [1] studied weakly prime ideals for a commutative ring with identity. Blair-Tsutsui [2] studied the structure of a ring in which every ideal is prime. In this paper we investigate the structure of rings, not necessarily commutative, in which all ideals are weakly prime.

Keywords: weakly prime

MSC numbers: 16N60, 16W99