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.
Acknowledgments
The authors would like to thank Gyu Whan Chang and Nematollah Shirmohammadi, for their comments on an earlier version of this paper.