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Localizing Systems and Semistar Operations

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Non-Noetherian Commutative Ring Theory

Part of the book series: Mathematics and Its Applications ((MAIA,volume 520))

Abstract

In 1994 A. Okabe and R. Matsuda [22] introduced the notion of semistar operation; see also, [21] and [20]. This concept extends the classical concept of star operation, as developed in Gilmer’s book [12], and hence the related classical theory of ideal systems based on the works of W. Krull, E. Noether, H. Prüfer, and P. Lorenzen from the 1930’s. For a systematic treatment of these ideas, see the books by P. Jaffard [17] and F. Halter-Koch [14], where a complete and updated bibliography is available.

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Fontana, M., Huckaba, J.A. (2000). Localizing Systems and Semistar Operations. In: Chapman, S.T., Glaz, S. (eds) Non-Noetherian Commutative Ring Theory. Mathematics and Its Applications, vol 520. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3180-4_8

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  • DOI: https://doi.org/10.1007/978-1-4757-3180-4_8

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4835-9

  • Online ISBN: 978-1-4757-3180-4

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