This article is cited in 1 scientific paper (total in 1 paper)
Polynomials, $\alpha$-ideals, and the principal lattice
Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan Republic
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.
almost distributive lattice, principal lattice, $\alpha$-ideals, multiplicative lattice, complete lattice, WB-height-unmixedness, Cohen–Macaulay rings, unmixedness.
PDF file (140 kB)
Received in revised form: 11.02.2011
Ali Molkhasi, “Polynomials, $\alpha$-ideals, and the principal lattice”, J. Sib. Fed. Univ. Math. Phys., 4:3 (2011), 292–297
Citation in format AMSBIB
\paper Polynomials, $\alpha$-ideals, and the principal lattice
\jour J. Sib. Fed. Univ. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
Ali Molkhasi, “The tensor product and quasiorder of an algebra related to Cohen–Macaulay rings”, Zhurn. SFU. Ser. Matem. i fiz., 8:1 (2015), 49–54
|Number of views:|