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Kyungpook Mathematical Journal 2020; 60(2): 307-318

Published online June 30, 2020

Copyright © Kyungpook Mathematical Journal.

Rings which satisfy the Property of Inserting Regular Elements at Zero Products

Hong Kee Kim, Tai Keun Kwak*, Yang Lee, Yeonsook Seo

Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea
e-mail : hkkim@gsnu.ac.kr
Department of Mathematics, Daejin University, Pocheon 11159, Korea
e-mail : tkkwak@daejin.ac.kr
Department of Mathematics, Yanbian University, Yanji 133002, China and Institute of Basic Science, Daejin University, Pocheon 11159, Korea
e-mail : ylee@pusan.ac.kr
Department of Mathematics, Pusan National University, Busan 46241, Korea
e-mail : ysseo0305@pusan.ac.kr

Received: October 22, 2019; Revised: January 21, 2020; Accepted: February 10, 2020

Abstract

This article concerns the class of rings which satisfy the property of inserting regular elements at zero products, and rings with such property are called regular-IFP. We study the structure of regular-IFP rings in relation to various ring properties that play roles in noncommutative ring theory. We investigate conditions under which the regular-IFPness pass to polynomial rings, and equivalent conditions to the regular-IFPness.

Keywords: regular-IFP ring, regular element, IFP ring, polynomial ring, generalized reduced ring