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Information Journal Paper

Title

Ideal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2]

Pages

  113-124

Abstract

 Let L and M be two finite lattices. The ideal J(L, M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ : L→ M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L, M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set of all lattice homomorphisms ϕ : L→ [2] according to the set of all lattice homomorphisms ϕ _1: L_1→ [2] and the set of all lattice homomorphisms ϕ _2: L_2→ [2]. Then, by using it and the set of associated prime ideals of both J(L_1, [2] ) and J(L_2, [2]), we study the associated prime ideals of J(L, [2]). Next, we assume that L_1=[2] and we characterized ass (J (L, [2])). Then by mapping cone technique and minimal free resolution of J(L_2, [2]), we find a free resolution of J(L, [2]) and an upper bound for the projective dimension of J(L, [2]). Finally, under the above assumptions and for the case that L_2=[n], we compute the minimal free resolution of J(L, [2]).

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    APA: Copy

    SHARIFAN, LEILA, & Malekbala, Ghazaleh. (2018). Ideal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2]. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 4(14 ), 113-124. SID. https://sid.ir/paper/257378/en

    Vancouver: Copy

    SHARIFAN LEILA, Malekbala Ghazaleh. Ideal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2]. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2018;4(14 ):113-124. Available from: https://sid.ir/paper/257378/en

    IEEE: Copy

    LEILA SHARIFAN, and Ghazaleh Malekbala, “Ideal of Lattice homomorphisms corresponding to the products of two arbitrary lattices and the lattice [2],” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 4, no. 14 , pp. 113–124, 2018, [Online]. Available: https://sid.ir/paper/257378/en

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