Star operations in extensions of integral domains

Anderson, David F.; El Baghdadi, Said; Zafrullah, Muhammad

doi:10.5802/acirm.39

David F. Anderson; Said El Baghdadi; Muhammad Zafrullah

Actes des rencontres du CIRM, Volume 2 (2010) no. 2, p. 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 : 2011-10-20
DOI : https://doi.org/10.5802/acirm.39
Classification: 13B02, 13A15, 13G05
Keywords: Star operation,

t

-linked,

t

-compatible, strongly

t

-compatible, domain extensions, Prüfer domain.

@article{ACIRM_2010__2_2_87_0,
     author = {David F. Anderson and Said El Baghdadi and Muhammad Zafrullah},
     title = {Star operations in extensions of integral domains},
     journal = {Actes des rencontres du CIRM},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     pages = {87-89},
     doi = {10.5802/acirm.39},
     language = {en},
     url = {https://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_87_0}
}

Anderson, David F.; El Baghdadi, Said; Zafrullah, Muhammad. 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://acirm.centre-mersenne.org/item/ACIRM_2010__2_2_87_0/

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