Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids

Jan Kühr

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2004)

  • Volume: 43, Issue: 1, page 105-112
  • ISSN: 0231-9721

Abstract

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Lattice-ordered groups, as well as G M V -algebras (pseudo M V -algebras), are both particular cases of dually residuated lattice-ordered monoids ( D R ℓ -monoids for short). In the paper we study ideals of lower-bounded D R ℓ -monoids including G M V -algebras. Especially, we deal with the connections between ideals of a D R ℓ -monoid A and ideals of the lattice reduct of A .

How to cite

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Kühr, Jan. "Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 43.1 (2004): 105-112. <http://eudml.org/doc/32357>.

@article{Kühr2004,
abstract = {Lattice-ordered groups, as well as $GMV$-algebras (pseudo $MV$-algebras), are both particular cases of dually residuated lattice-ordered monoids ($DR\ell $-monoids for short). In the paper we study ideals of lower-bounded $DR\ell $-monoids including $GMV$-algebras. Especially, we deal with the connections between ideals of a $DR\ell $-monoid $A$ and ideals of the lattice reduct of $A$.},
author = {Kühr, Jan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {$DR\ell $-monoid; ideal; prime ideal; DR-monoid; ideal; prime ideal},
language = {eng},
number = {1},
pages = {105-112},
publisher = {Palacký University Olomouc},
title = {Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids},
url = {http://eudml.org/doc/32357},
volume = {43},
year = {2004},
}

TY - JOUR
AU - Kühr, Jan
TI - Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2004
PB - Palacký University Olomouc
VL - 43
IS - 1
SP - 105
EP - 112
AB - Lattice-ordered groups, as well as $GMV$-algebras (pseudo $MV$-algebras), are both particular cases of dually residuated lattice-ordered monoids ($DR\ell $-monoids for short). In the paper we study ideals of lower-bounded $DR\ell $-monoids including $GMV$-algebras. Especially, we deal with the connections between ideals of a $DR\ell $-monoid $A$ and ideals of the lattice reduct of $A$.
LA - eng
KW - $DR\ell $-monoid; ideal; prime ideal; DR-monoid; ideal; prime ideal
UR - http://eudml.org/doc/32357
ER -

References

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  1. Cignoli R. L. O., Mundici D., D’Ottaviano I. M. L.: Algebraic Foundations of Many-valued Reasoning., Kluwer Acad. Publ., Dordrecht-Boston-London, , 2000. MR1786097
  2. Georgescu G., Iorgulescu A., Pseudo M V -algebras, Mult. Valued Log. 6 (2001), 95–135. Zbl1014.06008MR1817439
  3. Kovář T., A General Theory of Dually Residuated Lattice Ordered Monoids, Ph.D. Thesis, Palacký University, Olomouc, 1996. (1996) 
  4. Kühr J., Ideals of noncommutative D R ℓ -monoids, Czech. Math. J. (to appear). MR2121658
  5. Kühr J., Prime ideals and polars in D R ℓ -monoids and pseudo B L -algebras, Math. Slovaca 53 (2003), 233–246. MR2025020
  6. Kühr J., A generalization of G M V -algebras, (submitted). 
  7. Rachůnek J., D R ℓ -semigroups and M V -algebras, Czech. Math. J. 48 (1998), 365–372. (1998) MR1624268
  8. Rachůnek J., M V -algebras are categorically equivalent to a class of D R ℓ 1 ( i ) -semigroups, Math. Bohem. 123 (1998), 437–441. (1998) MR1667115
  9. Rachůnek J., Connections between ideals of non-commutative generalizations of M V -algebras and ideals of their underlying lattices, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 40 (2001), 195–200. Zbl1040.06005MR1904695
  10. Rachůnek J., A non-commutative generalization of M V -algebras, Czech. Math. J. 52 (2002), 255–273. Zbl1012.06012
  11. Swamy K. L. N., Dually residuated lattice ordered semigroups, Math. Ann. 159 (1965), 105–114. (1965) Zbl0138.02104MR0183797

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