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  • Tome 2 (2010)
  • no. 2
  • p. 87-89
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no. 2

Star operations in extensions of integral domains
David F. Anderson ; Said El Baghdadi ; Muhammad Zafrullah
Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 87-89.
  • Résumé

An extension D⊆R of integral domains is strongly t-compatible (resp., t-compatible) if (IR) -1 =(I -1 R) v (resp., (IR) 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⊆R is strongly t-compatible (resp., t-compatible) for every overring R of D.

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Publié le : 2011-10-20
DOI : https://doi.org/10.5802/acirm.39
Classification : 13B02,  13A15,  13G05
Mots clés : 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},
     pages = {87--89},
     publisher = {CIRM},
     volume = {2},
     number = {2},
     year = {2010},
     doi = {10.5802/acirm.39},
     language = {en},
     url = {https://acirm.centre-mersenne.org/articles/10.5802/acirm.39/}
}
Anderson, David F.; El Baghdadi, Said; Zafrullah, Muhammad. Star operations in extensions of integral domains. Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 87-89. doi : 10.5802/acirm.39. https://acirm.centre-mersenne.org/articles/10.5802/acirm.39/
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