
This article is cited in 1 scientific paper (total in 1 paper)
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 WBheightunmixed.
Keywords:
almost distributive lattice, principal lattice, $\alpha$ideals, multiplicative lattice, complete lattice, WBheightunmixedness, Cohen–Macaulay rings, unmixedness.
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UDC:
512.54 Received: 22.12.2010 Received in revised form: 11.02.2011 Accepted: 20.03.2011
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Ali Molkhasi, “Polynomials, $\alpha$ideals, and the principal lattice”, J. Sib. Fed. Univ. Math. Phys., 4:3 (2011), 292–297
Citation in format AMSBIB
\Bibitem{Mol11}
\by Ali~Molkhasi
\paper Polynomials, $\alpha$ideals, and the principal lattice
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 3
\pages 292297
\mathnet{http://mi.mathnet.ru/jsfu187}
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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

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