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HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGSHashem Bordbar,
Irina Cristea,
Michal Novak, 2017, izvirni znanstveni članek
Opis: Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. The main results in this note show that, in a commutative Noetherian Krasner hyperring, the height of a minimal prime hyperideal over a proper hyperideal generated by n elements is less than or equal to n, the converse of this claim being also true. Based on this result, it can be proved that the height of such a prime hyperideal is limited by the height of a corresponding quotient hyperideal.
Najdeno v: ključnih besedah
Povzetek najdenega: ...the class="IskanaBeseda">assicass="IskanaBeseda">al concept ass="IskanaBeseda">ass="Iskass="IskanaBeseda">anass="IskanaBeseda">aBesedass="IskanaBeseda">a">ass="IskanaBeseda">of ass="IskanaBeseda">ass="Iskass="IskanaBeseda">anass="IskanaBeseda">aBesedass="IskanaBeseda">a">ass="IskanaBeseda">height ass="IskanaBeseda">ass="Iskass="IskanaBeseda">anass="IskanaBeseda">aBesedass="IskanaBeseda">a">ass="IskanaBeseda">of ass="IskanaBeseda">a ass="IskanaBeseda">ass="Iskass="IskanaBeseda">anass="IskanaBeseda">aBesedass="IskanaBeseda">a">ass="IskanaBeseda">prime ideass="IskanaBeseda">al in ass="IskanaBeseda">a ring, we proposed in... ...the notion ass="IskanaBeseda">ass="Iskass="IskanaBeseda">anass="IskanaBeseda">aBesedass="IskanaBeseda">a">ass="IskanaBeseda">of ass="IskanaBeseda">ass="Iskass="IskanaBeseda">anass="IskanaBeseda">aBesedass="IskanaBeseda">a">ass="IskanaBeseda">height ass="IskanaBeseda">ass="Iskass="IskanaBeseda">anass="IskanaBeseda">aBesedass="IskanaBeseda">a">ass="IskKrasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Objavljeno: 01.06.2017; Ogledov: 3778; Prenosov: 0
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