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J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 3, Pages 292–297 (Mi jsfu187)  

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 WB-height-unmixed.

Keywords: almost distributive lattice, principal lattice, $\alpha$-ideals, multiplicative lattice, complete lattice, WB-height-unmixedness, Cohen–Macaulay rings, unmixedness.

Full text: PDF file (140 kB)
References: PDF file   HTML file
UDC: 512.54
Received: 22.12.2010
Received in revised form: 11.02.2011
Accepted: 20.03.2011
Language:

Citation: 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 292--297
\mathnet{http://mi.mathnet.ru/jsfu187}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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