Classification of monoids by injectivities II. CC-injectivity

We characterize monoids over which all S-acts are CC-injective and find conditions under which CC-injectivity of all acts implies that all acts are C-injective. Research of X. Zhang supported by the China Scholarship Council No. 2006101056. Research of Y. Chen supported by the NNSF of China (No. 10771077) and the NSF of Guangdong Province (No. 06025062).     

Classification of monoids by injectivities I. C-injectivity

A new kind of injectivity, namely, C-injectivity is investigated. Classifications of a monoid by properties of C-injective acts and right ideals are presented. It is shown that the class of monoids over which all acts are C-injective generalizes the class of self-injective monoids. On the way we complete an early result by Johnson and McMorris (Proc. Am. Math. Soc. 36(2), 385–388, 1972). Research of X. Zhang supported by the China Scholarship Council No. 2006101056. Research of Y. Chen supported by the NNSF of China (No. 10771077) and the NSF of Guangdong Province (No. 06025062).