{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:19Z","timestamp":1753893859714,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For two given finite lattices $L$ and $M$, we introduce the ideal of lattice homomorphism $J(L,M)$, whose minimal monomial generators correspond to lattice homomorphisms $\\phi : L\\to M$. We show that $L$ is a distributive lattice if and only if the equidimensinal part of $J(L,M)$ is the same as the equidimensional part of the ideal of poset homomorphisms $I(L,M)$. Next, we study the minimal primary decomposition of $J(L,M)$ when $L$ is a distributive lattice and $M=[2]$. We present some methods to check if a monomial prime ideal belongs to $\\mathrm{ass}(J(L,[2]))$, and we give an upper bound in terms of combinatorial properties of $L$ for the height of the minimal primes. We also show that if each minimal prime ideal of $J(L,[2])$ has height at most three, then $L$ is a planar lattice and $\\mathrm{width}(L)\\leq 2$. Finally, we compute the minimal primary decomposition when $L=[m]\\times [n]$ and $M=[2]$.<\/jats:p>","DOI":"10.37236\/7694","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:17:16Z","timestamp":1578651436000},"source":"Crossref","is-referenced-by-count":1,"title":["Primary Decomposition of Ideals of Lattice Homomorphisms"],"prefix":"10.37236","volume":"25","author":[{"given":"Leila","family":"Sharifan","sequence":"first","affiliation":[]},{"given":"Ali Akbar","family":"Estaji","sequence":"additional","affiliation":[]},{"given":"Ghazaleh","family":"Malekbala","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,7,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i3p8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:30:32Z","timestamp":1579217432000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i3p8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,13]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/7694","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,7,13]]},"article-number":"P3.8"}}