We study the properties of projective radicals of regular rings. It is shown that the projective radical of a regular ring is left-right symmetric and a regular ring modulo its projective radical has zero projective r...We study the properties of projective radicals of regular rings. It is shown that the projective radical of a regular ring is left-right symmetric and a regular ring modulo its projective radical has zero projective radical. Also, we obtain a relation between projective radicals of a finitely generated projective module over a regular ring and its endomorphism ring, from which we give formulas about projective radicals of matrix rings and corners of a regular ring, and some equivalent conditions for a regular ring with zero projective radicals are given.展开更多
文摘We study the properties of projective radicals of regular rings. It is shown that the projective radical of a regular ring is left-right symmetric and a regular ring modulo its projective radical has zero projective radical. Also, we obtain a relation between projective radicals of a finitely generated projective module over a regular ring and its endomorphism ring, from which we give formulas about projective radicals of matrix rings and corners of a regular ring, and some equivalent conditions for a regular ring with zero projective radicals are given.
