Invertibility, Semistar Operations, and the Ring of Finite Fractions

Kaiser A. Grap () and Jason R. Juett ()
Additional contact information
Kaiser A. Grap: University of Dubuque, Department of Computer Studies and Mathematics
Jason R. Juett: University of Dubuque, Department of Computer Studies and Mathematics

A chapter in Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, 2023, pp 213-236 from Springer

Abstract: Abstract Elliott and Lucas each introduced “Q0” variants of Dedekind rings, Krull rings, and Prüfer (v-multiplication) rings. These rings are defined analogously to their classical counterparts, but replacing (t-)invertibility in their total quotient ring with (t-)invertibility in their ring of finite fractions. We prove many new characterizations of (Q0-)Dedekind rings, (Q0-)Krull rings, strongly Prüfer rings, and (Q0-)Prüfer v-multiplication rings, and we generalize these results via (Q0-)semistar operations. We develop/refine several useful tools for working with (Q0-)semistar operations and answer a few open questions concerning t-linked overrings.

Keywords: Q0-Dedekind ring; Q0-Krull ring; Ring of finite fractions; Semistar operation; t-Linked overring; 13F05; 13A15; 13F15; 13A05 (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-28847-0_14

Ordering information: This item can be ordered from
http://www.springer.com/9783031288470

DOI: 10.1007/978-3-031-28847-0_14

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().