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On Primary Ideals in Posets

  • Vinayak Joshi EMAIL logo and Nilesh Mundlik
Published/Copyright: February 9, 2016
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Abstract

In this paper, we define the concepts of the radical of an ideal and a primary ideal in posets. Further, the analogue of the first and the second uniqueness theorems regarding primary decomposition of an ideal are obtained. In the last section, we prove that if an ideal in a poset Q has a minimal primary decomposition, then the diameter of the corresponding zero-divisor graph with respect to this ideal is exactly equal to three.

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Received: 2012-3-7
Accepted: 2013-6-4
Published Online: 2016-2-9
Published in Print: 2015-12-1

Mathematical Institute Slovak Academy of Sciences

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