Star operations in extensions of integral domains

David F. Anderson; Said El Baghdadi; Muhammad Zafrullah

doi:10.5802/acirm.39

David F. Anderson ¹; Said El Baghdadi ²; Muhammad Zafrullah ³

¹ Department of Mathematics, University of Tennessee Knoxville, TN 37996, USA
² Department of Mathematics, Faculté des Sciences et Techniques P.O. Box 523, Beni Mellal, Morocco
³ 57 Colgate Street, Pocatello, ID 83201, USA

Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 87-89.

Abstract

An extension $D \subseteq R$ of integral domains is strongly $t$ -compatible (resp., $t$ -compatible) if ${(I R)}^{- 1} = {(I^{- 1} R)}_{v}$ (resp., ${(I R)}_{v} = {(I_{v} R)}_{v})$ for every nonzero finitely generated fractional ideal $I$ of $D$ . We show that strongly $t$ -compatible implies $t$ -compatible and give examples to show that the converse does not hold. We also indicate situations where strong $t$ -compatibility and its variants show up naturally. In addition, we study integral domains $D$ such that $D \subseteq R$ is strongly $t$ -compatible (resp., $t$ -compatible) for every overring $R$ of $D$ .

Published online: 2011-10-19

Zbl: 06938587

DOI: 10.5802/acirm.39

Classification: 13B02, 13A15, 13G05
Keywords: Star operation, $t$-linked, $t$-compatible, strongly $t$-compatible, domain extensions, Prüfer domain.

Author's affiliations:

David F. Anderson ¹; Said El Baghdadi ²; Muhammad Zafrullah ³

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David F. Anderson; Said El Baghdadi; Muhammad Zafrullah. Star operations in extensions of integral domains. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 87-89. doi : 10.5802/acirm.39. https://pmb.cedram.org/articles/10.5802/acirm.39/

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