Geodesic
On $n$-Absorbing Ideals in a Lattice
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 4, p. 597

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Let $L$ be a lattice, and let $n$ be a positive integer. In this article, we introduce $n$-absorbing ideals in $L$. We give some properties of such ideals. We show that every $n$-absorbing ideal $I$ of $L$ has at most $n$ minimal prime ideals. Also, we give some properties of $2$-absorbing and weakly $2$-absorbing ideals in $L$. In particular we show that in every non-zero distributive lattice $L$, $2$-absorbing and weakly $2$-absorbing ideals are equivalent.
Classification : 03G10, 03G99
Keywords: lattice, minimal ideal, $2$-absorbing ideal, $n$-absorbing ideal 
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     author = {Ali Akbar Estaji and Toktam Haghdadi},
     title = {On $n${-Absorbing} {Ideals} in a {Lattice}},
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Ali Akbar Estaji; Toktam Haghdadi. On $n$-Absorbing Ideals in a Lattice. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 4, p. 597 . http://geodesic.mathdoc.fr/item/KJM_2021_45_4_a6/