A NOTE ON GORENSTEIN PRÜFER DOMAINS

A Note on Gorenstein Flat Dimension

Unlike the Gorenstein projective and injective dimensions, the majority of results on the Gorenstein flat dimension have been established only over Noetherian (or coherent) rings. Naturally, one would like to generalize these results to any associative ring. In this direction, we show that the Gorenstein flat dimension is a refinement of the classical flat dimension over any ring; and we invest...

A note on the problem when FS-domains coincide with RB-domains

In this paper, we introduce the notion of super finitely separating functions which gives a characterization of RB-domains. Then we prove that FS-domains and RB-domains are equivalent in some special cases by the following three claims: a dcpo is an RB-domain if and only if there exists an approximate identity for it consisting of super finitely separating functions; a consistent join-semilatti...

A "υ-Operation Free" Approach to Prüfer υ-Multiplication Domains

The so-called Prüfer υ-multiplication domains PυMDs are usually defined as domains whose finitely generated nonzero ideals are t-invertible. These domains generalize Prüfer domains and Krull domains. The PυMDs are relatively obscure compared to their verywell-known special cases. One of the reasons could be that the study of PυMDs uses the jargon of star operations, such as the υ-operation and ...

A note on Prüfer-like coding and counting forests of uniform hypertrees

The present note is designing encoding and decoding algorithms for a forest of rooted uniform hypertrees and hypercycles in linear time, by using as little as n− 2 integers in the range [1, n]. This simple extension of the classical Prüfer code for rooted trees to an encoding for forests of rooted uniform hypertrees and hypercycles makes it possible to count them up, according to their number o...

Note on Colon-Multiplication Domains