A structure theorem for right invariant right holoids

Abstract

aeR) of non-zero principal right ideals of a right chain domain R forms a semigroup with ideal multiplication as operation if and only if R is right invariant (i.e. all right ideals are two-sided). In this case, H(R) is a r.i.r. holoid and these semigroups play for right invariant right chain rings the role, that ordered groups play for invariant chain rings and commutative ordered groups for commutative valuation domains. Here, we prove a structure theorem (Theorem 3.1) for certain r.i.r. holoids of