This article is cited in 2 papers

Polynomials, $\alpha$-ideals, and the principal lattice

Ali Molkhasi

Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan Republic

Abstract: 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, multiplicative lattice, complete lattice, WB-height-unmixedness, Cohen–Macaulay rings, unmixedness.

UDC: 512.54

Received: 22.12.2010
Received in revised form: 11.02.2011
Accepted: 20.03.2011

Language: English