Graded almost pseudo-valuation domains

Abstract

Let Γ be a nonzero commutative cancellative monoid (written additively), be a Γ-graded integral domain with for all , and H be the set of nonzero homogeneous elements of R. A homogeneous ideal P of R will be said to be strongly homogeneous primary if implies or for some integer , for every homogeneous elements x, y of RH . We say that R is a graded almost pseudo-valuation domain (gr-APVD) if each homogeneous prime ideal of R is strongly homogeneous primary. In this paper, we study some ring-theoretic properties of gr-APVDs and graded integral domains R such that is a gr-APVD for all homogeneous maximal ideals (resp., homogeneous maximal t-ideals) P of R.