Characterizations of f-prime ideals in posets

Abstract

10 In this article, we look at the ideas of f -prime ideals and f -semi-prime 11 ideals of posets, as well as the many features of f -primeness and f -semi- 12 primeness in posets. Classifications of f semi-prime ideals in posets are 13 derived, as well as representations of a f -semi-prime ideal to be f -prime. 14 Furthermore, the f -prime ideal separation theorem is addressed.