环的正则性与内射性扩张

Extension of regularity and injectivity of rings

设I,K是环R的右理想,讨论了环R的平凡扩张R∝R具有右(I0,K0)-(m,n)-内射性(特别地,右(I0,K0)-n-内射性、右(I0,K0)-P-内射性、右(I0,K0)-FP-内射性)的充分条件,其中I0=I∝I,K0=K∝K.此外,本文还讨论了环R[A,B]具有强正则性、弱正则性的充要条件.

Let I,K be right ideas of ring R, various conditions are obtained for the trivial entension of R to be right （I°,K°）-（m,n） -injective （in particular, right （I°, K°）-n-injective, right （ I°, K°） -P-injective, right （I°,K°）-FP-injective）, where I°=I∝I,K°=K∝K. Besides, Some equivalent conditions that ring R[A,B] is trongly regular or weakly regular are given.