Quasi-Projective Covers and Direct Sums
نویسندگان
چکیده
منابع مشابه
Quasi-projective covers of right $S$-acts
In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...
متن کاملquasi-projective covers of right $s$-acts
in this paper $s$ is a monoid with a left zero and $a_s$ (or $a$) is a unitary right $s$-act. it is shown that a monoid $s$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $s$-act is quasi-projective. also it is shown that if every right $s$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that ...
متن کاملDirect Sums of Injective and Projective Modules
It is well-known that a countably injective module is Σ-injective. In Proc. Amer. Math. Soc. 316, 10 (2008), 3461-3466, Beidar, Jain and Srivastava extended it and showed that an injective module M is Σ-injective if and only if each essential extension of M(א0) is a direct sum of injective modules. This paper extends and simplifies this result further and shows that an injective module M is Σ-i...
متن کاملA generalization of projective covers
Let M be a left module over a ring R and I an ideal of R. We call (P,f ) a projective I -cover of M if f is an epimorphism from P to M , P is projective, Kerf ⊆ IP , and whenever P = Kerf + X, then there exists a summand Y of P in Kerf such that P = Y +X. This definition generalizes projective covers and projective δ-covers. Similar to semiregular and semiperfect rings, we characterize I -semir...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.2307/2037296