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Primary Ideals and Valuation Ideals in Semigroups |
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| Authors: | Mitsuo?Kanemitsu mailto:mkanemit@auecc.aichi-edu.ac.jp" title=" mkanemit@auecc.aichi-edu.ac.jp" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author,Hironao?Tanaka |
| Affiliation: | (1) Department of Mathematics, Aichi University of Education, Igaya-cho, Kariya-shi, 448–8542, JAPAN |
| Abstract: | Let S be a cancellation torsion-free additive semigroup with identity 0 and let S  {0}. We consider the relation between the valuation ideals and primary ideals of S. We give a characterization that each primary ideal is a valuation ideal in S and also give a characterization that each valuation ideal is a primary ideal in S.AMS Subject Classification (1991): 20M14 |
| Keywords: | valuation ideals of semigroups primary ideals of semigroups complete ideals of semigroups integral elements over semigroups |
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