For a Noetherian local domain (R, m, K), it is an open question whether strong F–regularity deforms. We provide an affirmative answer to this question when the canonical module satisfies certain additional assumptions. The techniques used here involve passing to a Gorenstein ring, using an anti– canonical cover.

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the de nitions of n-cleanness and n-f-cleanness are equivalent.

LUTHER Burbank was a curious mixture: part garStalin’s ear. He was arrested in 1940 while on a collecting trip and was sentenced to death, but this was rescinded dener, part artist, part P. T. Barnum. He was responsible for a plethora of improved fruits, vegetables, in June 1942. He died in prison in 1943. Had he been able to continue his program, he would surely have and ornamentals. Some of t...