Semiprime Ideals and Separation Theorems for Posets |
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| Authors: | Vilas S Kharat Khalid A Mokbel |
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| Institution: | (1) Department of Mathematics, University of Pune, Pune, 411 007, India |
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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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| Keywords: | Prime ideals Semiprime ideals Distributive posets etc |
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