关于幺半群上的n-主弱内射系

Let n be a positive integer. In this article a new kind ofinjectivity, namely n-principally weakly injective act is defined, this property is a genaralization of principally weakly injectivity. A monoid S is called n-regular, if for every s∈S, s n is regular. Using this new property the characterizations of category of n-regular monoids are investigated and some known results are extended.