On Primary Ideals in Posets

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.

The <img src=image/13426661_01.gif>-prime Radicals in Posets

“…Many authors studied the prime ideal concepts in posets [14,15,16,17,18,19,20]. Joshi [21] and John [22] later extended the primary ideal concept to posets. Considering [23,24], in this work, we investigate the concept of f -primary ideals in posets.…”