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Rachůnek, Jiří
Spectra of autometrized lattice algebras. (English). Mathematica Bohemica, vol. 123 (1998), issue 1, pp. 87-94
MSC: 06D20, 06F05, 06F20 | MR 1618727 | Zbl 0897.06017 | DOI: 10.21136/MB.1998.126293
Keywords:
autometrized algebra; dually residuated lattice ordered semigroup; prime ideal; spectrum; lattice-ordered algebras
Summary:
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.
References:
[1] Hаnsen M. E.: Minimal prime ideals in autometrized algebras. Czechoslovak Math. J. 44 (119) (1994), 81-90. MR 1257938
[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. MR 0875128
[5] Rаchůnek J.: Polars in autometrized algebras. Czechoslovak Math. J. 39 (114) (1989), 681-685. MR 1018003
[6] Rаchůnek J.: Regular ideals in autometrized algebras. Math. Slovaca 40 (1990), 117-122. MR 1094766
[7] Swаmy K. L. N.: A general theory of autometrized algebras. Math. Ann. 157 (1964), 65-74. DOI 10.1007/BF01362667 | MR 0170842
[8] Swаmy K. L. N.: Dually residuated lattice ordered semigroups. Math. Ann. 159 (1965), 105-114. DOI 10.1007/BF01360284 | MR 0183797
[9] Swаmy K. L. N., Rаo N. P.: Ideals in autometrized algebras. J. Austral. Math. Soc. (Ser. A) 24 (1977), 362-374. DOI 10.1017/S1446788700020383 | MR 0469843
[10] Swаmy K. L. N., Subbа Rаo B. V.: Isometries in dually residuated lattice ordered semigroups. Math. Sem. Notes Kobe 8 (1980), 369-380. MR 0601906
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