Note on the number of semistar operations, VIII
Ryûki Matsuda · Mathematical journal of Ibaraki University · 2005
We concern with the number of star operations or of semistar operations on an integral domain or on a semigroup.Since all the proofs in [M 4,7,8] and [MS] are not necessarily complete, it is necessary for us to make a self-contained, well got together and systematically written paper on the subject.Some results in this paper are new.We confer Badawi-Houston [BH], Hedstrom-Houston [HH], Heinzer [H], and many other references.Throughout the paper, D denotes an integral domain, and S denotes a nonzero g-monoid.A g-monoid means a submonoid of a torsion-free abelian additive group.