Title:
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Spectral topologies of dually residuated lattice-ordered monoids (English) |
Author:
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Kühr, Jan |
Language:
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English |
Journal:
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Mathematica Bohemica |
ISSN:
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0862-7959 (print) |
ISSN:
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2464-7136 (online) |
Volume:
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129 |
Issue:
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4 |
Year:
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2004 |
Pages:
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379-391 |
Summary lang:
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English |
. |
Category:
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math |
. |
Summary:
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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. (English) |
Keyword:
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$DR\ell $-monoid |
Keyword:
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prime ideal |
Keyword:
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spectrum |
MSC:
|
03G10 |
MSC:
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03G25 |
MSC:
|
06D35 |
MSC:
|
06F05 |
idZBL:
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Zbl 1080.06023 |
idMR:
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MR2102611 |
DOI:
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10.21136/MB.2004.134046 |
. |
Date available:
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2009-09-24T22:16:31Z |
Last updated:
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2020-07-29 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/134046 |
. |
Reference:
|
[1] R. Balbes, P. Dwinger: Distributive Lattices.University of Missouri Press, Columbia, 1974. MR 0373985 |
Reference:
|
[2] R. L. O. Cignoli, I. M. L. D’Ottawiano, D. Mundici: Algebraic Foundations of Many-Valued Reasoning.Kluwer, Dordrecht, 2000. |
Reference:
|
[3] A. Di Nola, G. Georgescu, A. Iorgulescu: Pseudo $BL$-algebras: Part I.Mult. Valued Log. 8 (2002), 673–714. MR 1948853 |
Reference:
|
[4] A. Di Nola, G. Georgescu, A. Iorgulescu: Pseudo $BL$-algebras: Part II.Mult. Valued Log. 8 (2002), 717–750. MR 1948854 |
Reference:
|
[5] R. Engelking: General Topology.PWN, Warszawa, 1977. Zbl 0373.54002, MR 0500780 |
Reference:
|
[6] G. Georgescu, A. Iorgulescu: Pseudo $MV$-algebras.Mult. Valued Log. 6 (2001), 95–135. MR 1817439 |
Reference:
|
[7] A. M. W. Glass: Partially Ordered Groups.World Scientific, Singapore, 1999. Zbl 0933.06010, MR 1791008 |
Reference:
|
[8] P. Hájek: Metamathematics of Fuzzy Logic.Kluwer, Dordrecht, 1998. MR 1900263 |
Reference:
|
[9] P. Hájek: Basic fuzzy logic and $BL$-algebras.Soft Comput. 2 (1998), 124–128. 10.1007/s005000050043 |
Reference:
|
[10] T. Kovář: A General Theory of Dually Residuated Lattice Ordered Monoids.Ph.D. Thesis, Palacký Univ., Olomouc, 1996. |
Reference:
|
[11] J. Kühr: Ideals of non-commutative $DR\ell $-monoids.(to appear). |
Reference:
|
[12] J. Kühr: Prime ideals and polars in $DR\ell $-monoids and pseudo $BL$-algebras.Math. Slovaca 53 (2003), 233–246. MR 2025020 |
Reference:
|
[13] J. Rachůnek: Spectra of autometrized lattice algebras.Math. Bohem. 123 (1998), 87–94. MR 1618727 |
Reference:
|
[14] J. Rachůnek: $MV$-algebras are categorically equivalent to a class of $DR\ell _{1(i)}$-semigroups.Math. Bohem. 123 (1998), 437–441. MR 1667115 |
Reference:
|
[15] J. Rachůnek: A duality between algebras of basic logic and bounded representable $DR\ell $-monoids.Math. Bohem. 126 (2001), 561–569. MR 1970259 |
Reference:
|
[16] J. Rachůnek: A non-commutative generalization of $MV$-algebras.Czechoslovak Math. J. 52 (2002), 255–273. Zbl 1012.06012, MR 1905434, 10.1023/A:1021766309509 |
Reference:
|
[17] J. Rachůnek: Prime spectra of non-commutative generalizations of $MV$-algebras.Algebra Univers. 48 (2002), 151–169. Zbl 1058.06015, MR 1929902, 10.1007/PL00012447 |
Reference:
|
[18] J. T. Snodgrass, C. Tsinakis: Finite-valued algebraic lattices.Algebra Univers. 30 (1993), 311–318. MR 1225870 |
Reference:
|
[19] K. L. N. Swamy: Dually residuated lattice ordered semigroups I.Math. Ann. 159 (1965), 105–114. MR 0183797, 10.1007/BF01360284 |
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