Keywords:-

Keywords: Finite lattices, Non-distributive non-modular lattices, Join-meet ideal, Radical ideal, Compatible monomial order, Gröbner basis

Article Content:-

Abstract

For non-distributive lattice L, it is not yet known classes of L with the property that the join-meet ideal of L is radical. In this paper, we give a partial answer to this problem.

References:-

References

J. Herzog, T. Hibi, H. Ohsugi, Binomial Ideals, Springer(2018).

V. Ene, Takayuki Hibi, The join-meet ideal of a finite lattice, J. Commut. Algebra 5 (2013), no. 2 , 209–230.

T. Hibi, Distributive lattices, affine semigroup rings and algebras with straightening laws, in“ Commutative Algebra and Combinatorics”(M. Nagata and H. Matsumura, Eds.), Advanced Studies in Pure Math., Volume 11, North–Holland, Amsterdam, 1987, pp. 93 – 109.

M. Noro, N. Takayama, H. Nakayama, K. Nishiyama, K. Ohara. Risa/Asir: A computer algebra system. http://www.math.kobe-u.ac.jp/Asir/asir.html.

Graduate School of Engineering and Science , Shibaura Institute of Technology, 307 Minumaku Fukasaku, Saitama-City 337-8570, Japan.

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Oshida, Y. (2022). New Examples of Radical Join-Meet Ideals. International Journal Of Mathematics And Computer Research, 10(2), 2590-2602. https://doi.org/10.47191/ijmcr/v10i2.07