Maximal and essential ideas of MV-algebras
Mathware & soft computing, 1995
Online
academicJournal
Zugriff:
We show that an atom free ideal is densely ordered. It is shown that if $I$ is a maximal ideal of an $MV\mbox{-algebra}\;A,$ then =I^\perp\oplus I^{\perp\perp}$ where $I^\perp=\{x\vert x\le e\}$ and $I^{\perp\perp} =\{x\vert x\le \bar e\}$ for a unique idempotent $e.$ The socle, radical and implicative radical of $A$ are computed in certain cases. It is shown that if $A$ is not atom free but $I$ is a maximal ideal which is atom free, then $I$ is densely ordered, and $I=\la At(A)\ra^\perp=\la a\ra^\perp$ where $At(A)$ is the set of atoms of $A$ and $a\in At(A).$ Then $A=I^\perp\oplus I^{\perp\perp}$ where $I^\perp$ is atomic and $I^{\perp\perp}$ is atom free.
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Maximal and essential ideas of MV-algebras
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Autor/in / Beteiligte Person: | Hoo, C. S. |
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Veröffentlichung: | Mathware & soft computing, 1995 |
Medientyp: | academicJournal |
ISSN: | 1989-533X (print) ; 1134-5632 (print) |
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