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 ...

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 ...

We define a quasi–projective reduction of a complex algebraic variety X to be a regular map from X to a quasi–projective variety that is universal with respect to regular maps from X to quasi–projective varieties. A toric quasi–projective reduction is the analogous notion in the category of toric varieties. For a given toric variety X we first construct a toric quasi–projective reduction. Then ...

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is generalization of projective dimension. We discuss various properties Among other things, prove the following. (1) Over quotient regular local ring by sequence, every finitely generated module has finite (2) The Auslander--Buchsbaum formula and depth for modules dimension remain valid (3) Several...

This moduli space is Mh = Γ \Dh where Dh = GR/V is a homogeneous complex manifold on which Γ acts properly discountinuously. In the classical case n = 1 (polarized abelian varieties) or n = 2, h = 1, D is a bounded symmetric domain and Γ \D is a quasi-projective variety defined over a number field. In the non-classical case the situation is quite different. Given a smooth projective family X π ...

Blaine Lawson and the author introduced algebraic cocycles on complex algebraic varieties in [FL-1] and established a duality theorem relating spaces of algebraic cocycles and spaces of algebraic cycles in [FL-2]. This theorem has non-trivial (and perhaps surprising) applications in several contexts. In particular, duality enables computations of “algebraic mapping spaces” consisting of algebra...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.