EXTENSIONS OF STRONGLY π-REGULAR RINGS
EXTENSIONS OF STRONGLY π-REGULAR RINGS
An ideal I of a ring R is strongly <TEX>${\pi}$</TEX>-regular if for any <TEX>$x{\in}I$</TEX> there exist <TEX>$n{\in}\mathbb{N}$</TEX> and <TEX>$y{\in}I$</TEX> such that <TEX>$x^n=x^{n+1}y$</TEX>. We prove that every strongly <TEX>${\pi}$</TEX>-regular ideal of a ring is a B-ideal. An ideal I is periodic provided that for any <TEX>$x{\in}I$</TEX> there exist two distinct m, …