Homogeneously t-linked extensions in graded integral domains

Abstract

Let [Formula: see text] be a torsion-free cancellative commutative monoid, [Formula: see text] a graded integral domain and [Formula: see text] a graded subring of [Formula: see text]. Then we say that [Formula: see text] is homogeneously[Formula: see text]-linked over [Formula: see text] if for any nonzero finitely generated homogeneous ideal [Formula: see text] of [Formula: see text] such that [Formula: see text], [Formula: see text]. In this paper, we introduce some examples of homogeneously [Formula: see text]-linked extensions and offer some equivalent conditions for homogeneously [Formula: see text]-linked extensions. More precisely, we provide some equivalent conditions such that every graded subring of [Formula: see text] containing [Formula: see text] is homogeneously [Formula: see text]-linked over [Formula: see text]; and offer some new characterizations of graded Krull domains.