Commun. Korean Math. Soc. 2002 Vol. 17, No. 2, 229-235 Printed June 1, 2002
Sun Shin Ahn and Hee Sik Kim Dongguk University, Hanyang University
Abstract : In this paper we show that if $\Cal K$ is an incline with multiplicative identity and $I$ is an $r$-ideal of $\Cal K$ containing a unit $u$, then $I=\Cal K$. Moreover, we show that in a non-zero incline $\Cal K$ with multiplicative identity and zero element, every proper $r$-ideal in $\Cal K$ is contained in a maximal $r$-ideal of $\Cal K$.
Keywords : incline, field incline, $r$-ideal, maximal ideal, annihilator