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Semiprime Ideals and Separation Theorems for Posets

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Abstract

The concept of a semiprime ideal in a poset is introduced. The relations between the semiprime (prime) ideals of a poset and the ideals of the set of all ideals of the poset are established. A result analogous to Separation Theorem is obtained in respect of semiprime ideals. Further, a generalization of Stone’s Separation Theorem for posets is obtained in respect of prime ideals. Some counterexamples are also given.

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  1. Department of Mathematics, University of Pune, Pune, 411 007, India

    Vilas S. Kharat & Khalid A. Mokbel

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  1. Vilas S. Kharat
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  2. Khalid A. Mokbel
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Correspondence to Khalid A. Mokbel.

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Kharat, V.S., Mokbel, K.A. Semiprime Ideals and Separation Theorems for Posets. Order 25, 195–210 (2008). https://doi.org/10.1007/s11083-008-9087-3

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  • DOI: https://doi.org/10.1007/s11083-008-9087-3

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