Quasi-projective dimension

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 ...

Bounding Projective Dimension

The use of algorithms in algebra as well as the study of their complexity was initiated before the advent of modern computers. Hermann [25] studied the ideal membership problem, i.e determining whether a given polynomial is in a fixed homogeneous ideal, and found a doubly exponential bound on its computational complexity. Later Mayr and Meyer [31] found examples which show that her bound was ne...

Finitistic Dimension through Infinite Projective Dimension

We show that an artin algebra Λ having at most three radical layers of infinite projective dimension has finite finitistic dimension, generalizing the known result for algebras with vanishing radical cube. We also give an equivalence between the finiteness of fin.dim.Λ and the finiteness of a given class of Λ-modules of infinite projective dimension.

Non – Quasi – Projective

Finite Flat and Projective Dimension

known as the left big finitistic projective dimension of A, is finite. Here pdM denotes the projective dimension of M . Unfortunately, this number is not known to be finite even if A is a finite dimensional algebra over a field, where, indeed, its finiteness is a celebrated conjecture. On the other hand, for such an algebra, finite flat certainly implies finite projective dimension, simply beca...