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On v-domains: a survey

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Abstract

An integral domain D is a v-domain if, for every finitely generated nonzero (fractional) ideal F of D, we have (FF −1)−1=D. The v-domains generalize Prüfer and Krull domains and have appeared in the literature with different names. This paper is the result of an effort to put together information on this useful class of integral domains. In this survey, we present old, recent and new characterizations of v-domains along with some historical remarks. We also discuss the relationship of v-domains with their various specializations and generalizations, giving suitable examples.

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  1. Dipartimento di Matematica, Università degli Studi “Roma Tre”, 00146, Roma, Italy

    Marco Fontana

  2. 57 Colgate Street, Pocatello, ID, 83201, USA

    Muhammad Zafrullah

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  1. , Dipartimento di Matematica, Università degli Studi Roma Tre, Largo San Leonardo Murialdo 1, Roma, 00146, Italy

    Marco Fontana

  2. , Department of Mathematics and Statistics, King Fahd University of Petroleum & Mine, Dhahran, 31261, Saudi Arabia

    Salah-Eddine Kabbaj

  3. , Department of Mathematical Sciences, New Mexico State University, Las Cruces, 88003, New Mexico, USA

    Bruce Olberding

  4. , Department of Mathematics, Reed College, Southeast Woodstock Blvd. 3203, Portland, 97202-8199, Oregon, USA

    Irena Swanson

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Fontana, M., Zafrullah, M. (2011). On v-domains: a survey. In: Fontana, M., Kabbaj, SE., Olberding, B., Swanson, I. (eds) Commutative Algebra. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6990-3_6

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