ON THE QUOTIENT RING OF COMMUTATIVE RINGS WITH ACC PERPENDICULAR-TO ON ANNIHILATOR IDEALS

The author concludes that every commutative ring with ascending chain condition on annihilator ideals has a Kasch quotient ring, which generalizes the Theorem[1] that every commutative noetherian ring has a Kasch quosient ring. If follows that if R is a commutative ring with acc perpendicular-to, then that Q(R) is semiprimary is equivalent to that it is perfect, or to that R satisfies regular condition. Besides, that Q(R) is quasi-frobenius equals that Q(R) is FPF or PF, and that Q(R) is artinian equals that R/N(i) are of finite dimension, i = 1, 2, ..., n. N(i) = J(i) intersect R.