Quasi-projective covers of right S-acts

Abstract. In this paper S is a monoid with a left zero and AS (or A) is a
unitary right S-act. It is shown that a monoid S is right perfect (semiperfect)
if and only if every (nitely generated) strongly
at right S-act is quasiprojective.
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
every right act has a projective cover.
Projective, quasi-projective, perfect, semiperfect, cover. Mathematics Subject Classication [2010]: 20M30, 20M50.



J. Ahsan and K. Saifullah, Completely quasi-projective monoids, Semigroup Forum

(1989), 123-126.

J. Fountain, Perfect semigroups, Proc. Edinburgh Math. Soc. 20(3) (1976), 87-93.

J. Isbell, Perfect monoids, Semigroup Forum 2 (1971), 95-118.

R. Khosravi, M. Ershad, and M. Sedaghatjoo, Storngly

at and condition (P) covers

of acts over monoids, Comm. Algebra 38(12) (2010), 4520-4530.

M. Kilp, U. Knauer, and A. Mikhalev, Monoids, Acts and Categories, With Application

to Wreath Products and Graphs"; Berlin, New York, 2000.

Quasi-projective covers of right S-acts 45

U. Knauer and H. Oltmanns, On Rees weakly projective right acts, J. Math. Sci.

(4) (2006), 6715-6722.

U. Knauer and H. Oltmanns, Weak projectivities for S-acts, Proceeding of the Conference

on General Algebra and Discrete Math. (postsdam), Aachen (1999), 143-159.

M. Mahmoudi and J. Renshaw, On covers of cyclic acts over monoids, Semigroup

Forum 77 (2008), 325-338.

J. Wei, On a question of Kilp and Knauer, Comm. Algebra 32(6) (2004), 2269-2272.

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