MATHEMATICA BOHEMICA, Vol. 129, No. 4, pp. 379-391 (2004)

Spectral topologies of dually residuated lattice-ordered monoids

Jan K\"{u}hr

{\it Jan K\"{u}hr}, Department of Algebra and Geometry, Faculty of Science, Palacky University, Tomkova 40, 779 00 Olomouc, Czech Republic, e-mail:

Abstract: Dually residuated lattice-ordered monoids ($DR\ell$-monoids for short) generalize lattice-ordered groups and include for instance also $GMV$-algebras (pseudo $MV$-algebras), a non-commutative extension of $MV$-algebras. In the present paper, the spectral topology of proper prime ideals is introduced and studied.

Keywords: $DR\ell$-monoid, prime ideal, spectrum

Classification (MSC2000): 06F05, 03G25

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