Spectra of autometrized lattice algebras

Jiří Rachůnek

Mathematica Bohemica (1998)

  • Volume: 123, Issue: 1, page 87-94
  • ISSN: 0862-7959

Abstract

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Autometrized algebras are a common generalization e.g. of commutative lattice ordered groups and Brouwerian algebras. In the paper, spectra of normal autometrized lattice ordered algebras (i.e. topologies of sets (and subsets) of their proper prime ideals) are studied. Especially, the representable dually residuated lattice ordered semigroups are examined.

How to cite

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Rachůnek, Jiří. "Spectra of autometrized lattice algebras." Mathematica Bohemica 123.1 (1998): 87-94. <http://eudml.org/doc/248308>.

@article{Rachůnek1998,
abstract = {Autometrized algebras are a common generalization e.g. of commutative lattice ordered groups and Brouwerian algebras. In the paper, spectra of normal autometrized lattice ordered algebras (i.e. topologies of sets (and subsets) of their proper prime ideals) are studied. Especially, the representable dually residuated lattice ordered semigroups are examined.},
author = {Rachůnek, Jiří},
journal = {Mathematica Bohemica},
keywords = {autometrized algebra; dually residuated lattice ordered semigroup; prime ideal; spectrum; lattice-ordered algebras; autometrized algebra; dually residuated lattice ordered semigroup; prime ideal; spectrum; lattice-ordered algebras},
language = {eng},
number = {1},
pages = {87-94},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Spectra of autometrized lattice algebras},
url = {http://eudml.org/doc/248308},
volume = {123},
year = {1998},
}

TY - JOUR
AU - Rachůnek, Jiří
TI - Spectra of autometrized lattice algebras
JO - Mathematica Bohemica
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 123
IS - 1
SP - 87
EP - 94
AB - Autometrized algebras are a common generalization e.g. of commutative lattice ordered groups and Brouwerian algebras. In the paper, spectra of normal autometrized lattice ordered algebras (i.e. topologies of sets (and subsets) of their proper prime ideals) are studied. Especially, the representable dually residuated lattice ordered semigroups are examined.
LA - eng
KW - autometrized algebra; dually residuated lattice ordered semigroup; prime ideal; spectrum; lattice-ordered algebras; autometrized algebra; dually residuated lattice ordered semigroup; prime ideal; spectrum; lattice-ordered algebras
UR - http://eudml.org/doc/248308
ER -

References

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  1. Hаnsen M. E., Minimal prime ideals in autometrized algebras, Czechoslovak Math. J. 44 (119) (1994), 81-90. (1994) MR1257938
  2. Hаnsen M. E., Filets and z-ideals in autometrized algebras, Preprint. 
  3. Kovář T., Normal autometrized l-algebras, Preprint. 
  4. Rаchůnek J., Prime ideals in autometrized algebras, Czechoslovak Math. J. 37 (112) (1987), 65-69. (1987) MR0875128
  5. Rаchůnek J., Polars in autometrized algebras, Czechoslovak Math. J. 39 (114) (1989), 681-685. (1989) MR1018003
  6. Rаchůnek J., Regular ideals in autometrized algebras, Math. Slovaca 40 (1990), 117-122. (1990) MR1094766
  7. Swаmy K. L. N., 10.1007/BF01362667, Math. Ann. 157 (1964), 65-74. (1964) MR0170842DOI10.1007/BF01362667
  8. Swаmy K. L. N., 10.1007/BF01360284, Math. Ann. 159 (1965), 105-114. (1965) MR0183797DOI10.1007/BF01360284
  9. Swаmy K. L. N., Rаo N. P., 10.1017/S1446788700020383, J. Austral. Math. Soc. (Ser. A) 24 (1977), 362-374. (1977) MR0469843DOI10.1017/S1446788700020383
  10. Swаmy K. L. N., Subbа Rаo B. V., Isometries in dually residuated lattice ordered semigroups, Math. Sem. Notes Kobe 8 (1980), 369-380. (1980) MR0601906

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