Geodesic
Characterizations of $f$-prime ideals in posets
Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 413-426

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In this article, we look at the ideas of f-prime ideals and f-semi-prime ideals of posets, as well as the many features of f-primeness and f-semi-primeness in posets. Classifications of f semi-prime ideals in posets are derived, as well as representations of a f semi-prime ideal to be f prime. Furthermore, the f-prime ideal separation theorem is addressed.
Keywords: poset, semi-ideals, $f$-prime ideal, $f$-semi prime ideal, $m$-system 
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John, J. Catherine Grace; Veninstine Vivik, J.; Divya, P.S. Characterizations of $f$-prime ideals in posets. Discussiones Mathematicae. General Algebra and Applications, Tome 44 (2024) no. 2, pp. 413-426. http://geodesic.mathdoc.fr/item/DMGAA_2024_44_2_a10/