More on Prime, Maximal and Principal Soft Ideals of Soft Rings

Abstract

In this paper, we aim to extend the studies [M. R.. Alimoradi, R.. Rezaei and M. Rahimi, Some notes on ideals in soft rings, Journal Australian Journal of Basic and Applied Sciences 6(3) (2012) 717-721; F. Koyuncu and B. Tanay, Some soft algebraic structures, Journal of New Results Science 10 (2016) 38-51] as regards maximal, prime and principal soft ideal of soft rings, characterize soft rings with these soft ideals and also provide some more relations between maximal, prime and principal soft ideals of soft rings. The notions of maximality and primeness points of soft ideals of a soft rings are defined, maximal and prime idealistic soft rings as well as maximal, prime and principal soft ideal of soft rings and their basic properties are more investigated under certain conditions, especially by means of homomorphism and epimorphism of rings. We apply some of the basic results about maximal ideals and prime ideals in classical abstract algebra to maximal, prime and principal idealistic soft rings and we give some of their interrelations between each others.