Geodesic
Polynomials, $\alpha$-ideals, and the principal lattice
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 3, pp. 292-297

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Let $R$ be a commutative ring with an identity, $\mathfrak R$ be an almost distributive lattice and $I_\alpha(\mathfrak R)$ be the set of all $\alpha$-ideals of $\mathfrak R$. If $L(R)$ is the principal lattice of $R$, then $R[I_\alpha(\mathfrak R)]$ is Cohen–Macaulay. In particular, $R[I_\alpha(\mathfrak R)][X_1,X_2,\cdots]$ is WB-height-unmixed.
Keywords: almost distributive lattice, principal lattice, $\alpha$-ideals, complete lattice, WB-height-unmixedness, Cohen–Macaulay rings, unmixedness.
Mots-clés : multiplicative lattice 
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     title = {Polynomials, $\alpha$-ideals, and the principal lattice},
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Ali Molkhasi. Polynomials, $\alpha$-ideals, and the principal lattice. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 3, pp. 292-297. http://geodesic.mathdoc.fr/item/JSFU_2011_4_3_a2/