Primes and Right Ideals in Right Cones |
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| Authors: | H H Brungs |
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| Institution: | 1. Department of Mathematical &2. Statistical Sciences , University of Algebra , Edmonton, Canada |
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| Abstract: | A right cone H in a group G is a submonoid of G that generates G and aH ? bH for a, b ? H implies bH ? aH. With any right ideal I ≠ H of H a completely prime ideal P r (I) of H is associated and the set 𝒫(I) of right ideals I′ of H with the same associated prime ideal P′ =P r (I) is determined if P′·? P″ is a right invariant segment in H. The set 𝒫(I) is also described if P r (I) is a limit prime. |
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| Keywords: | I-Compactness Completion Limit prime ideal Ordered semigroup Prime ideal Right chain domain Right cone Valuation ring |
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