On $n$-Absorbing Ideals in a Lattice
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Authors: A. A. ESTAJI AND T. HAGHDADI
DOI: 10.46793/KgJMat2104.597E
Abstract:
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.
Keywords:
Lattice, minimal ideal, 2-absorbing ideal, n-absorbing ideal.
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