THE PRIME SPECTRUM ON BL-ALGEBRAS AND MV-ALGEBRAS

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ESLAMI E.; HAGHANI F.KH.

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Seminar Paper

Paper Information

Seminar: IRANIAN ALGEBRA SEMINAR
Year:2009 | Issue:20

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Title

THE PRIME SPECTRUM ON BL-ALGEBRAS AND MV-ALGEBRAS

Author(s)

ESLAMI E. | HAGHANI F.KH.

Keywords

MV-ALGEBRA

BL-ALGEBRA

SPECTRAL TOPOLOGY

PRIME SPECTRUM

Abstract

IN 1958 C. C. CHANG DEVELOPED AN ALGEBRAIC VERSION OF LUKASIEWICZ PROPOSITIONAL LOGIC AND PROVIDED AN ALGEBRAIC PROOF OF THE COMPLETENESS. THE RESULTING ALGEBRAIC SYSTEM BECAME KNOWN AS AN MV-ALGEBRA. IN 1998 PETER H´AJEK INTRODUCED THE VARIETY OF BL-ALGEBRAS AND SHOWED THAT THE VARIETY OF MV-ALGEBRAS ACTUALLY IS A SUBVARIETY OF THE VARIETY OF BL-ALGEBRAS.IN OTHER WORDS, ANY MV-ALGEBRA CAN BE EASILY VIEWED AS A SPECIAL BL-ALGEBRA. LET A BE AN MV-ALGEBRA. WE DENOTE BY SPEC (A) THE SET OF PRIME IDEALS OF A. SPEC (A) CAN BE ENDOWED WITH A SPECTRAL TOPOLOGY IN THE SAME MANNER AS IN THE CASE OF A COMMUTATIVE RING OR A BOUNDED DISTRIBUTIVE LATTICE. HOWEVER THE ABSENCE OF A DISTRIBUTIVE LAW REQUIERS A REFORMULATION OF THE RESULTS KNOWN IN RING THEORY. THUS IT MAKES SENSE TO GENERALIZE THE NOTION OF PRIME SPECTRUM TO BL-ALGEBRAS.

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APA: Copy

ESLAMI, E., & HAGHANI, F.KH.. (2009). THE PRIME SPECTRUM ON BL-ALGEBRAS AND MV-ALGEBRAS. IRANIAN ALGEBRA SEMINAR. SID. https://sid.ir/paper/904420/en

Vancouver: Copy

ESLAMI E., HAGHANI F.KH.. THE PRIME SPECTRUM ON BL-ALGEBRAS AND MV-ALGEBRAS. 2009. Available from: https://sid.ir/paper/904420/en

IEEE: Copy

E. ESLAMI, and F.KH. HAGHANI, “THE PRIME SPECTRUM ON BL-ALGEBRAS AND MV-ALGEBRAS,” presented at the IRANIAN ALGEBRA SEMINAR. 2009, [Online]. Available: https://sid.ir/paper/904420/en

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