| Title:
|
Spectra of autometrized lattice algebras (English) |
| Author:
|
Rachůnek, Jiří |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
87-94 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
autometrized algebra |
| Keyword:
|
dually residuated lattice ordered semigroup |
| Keyword:
|
prime ideal |
| Keyword:
|
spectrum |
| Keyword:
|
lattice-ordered algebras |
| MSC:
|
06D20 |
| MSC:
|
06F05 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 0897.06017 |
| idMR:
|
MR1618727 |
| DOI:
|
10.21136/MB.1998.126293 |
| . |
| Date available:
|
2009-09-24T21:29:35Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126293 |
| . |
| Reference:
|
[1] Hаnsen M. E.: Minimal prime ideals in autometrized algebras.Czechoslovak Math. J. 44 (119) (1994), 81-90. MR 1257938 |
| Reference:
|
[2] Hаnsen M. E.: Filets and z-ideals in autometrized algebras.Preprint. |
| Reference:
|
[3] Kovář T.: Normal autometrized l-algebras.Preprint. |
| Reference:
|
[4] Rаchůnek J.: Prime ideals in autometrized algebras.Czechoslovak Math. J. 37 (112) (1987), 65-69. MR 0875128 |
| Reference:
|
[5] Rаchůnek J.: Polars in autometrized algebras.Czechoslovak Math. J. 39 (114) (1989), 681-685. MR 1018003 |
| Reference:
|
[6] Rаchůnek J.: Regular ideals in autometrized algebras.Math. Slovaca 40 (1990), 117-122. MR 1094766 |
| Reference:
|
[7] Swаmy K. L. N.: A general theory of autometrized algebras.Math. Ann. 157 (1964), 65-74. MR 0170842, 10.1007/BF01362667 |
| Reference:
|
[8] Swаmy K. L. N.: Dually residuated lattice ordered semigroups.Math. Ann. 159 (1965), 105-114. MR 0183797, 10.1007/BF01360284 |
| Reference:
|
[9] Swаmy K. L. N., Rаo N. P.: Ideals in autometrized algebras.J. Austral. Math. Soc. (Ser. A) 24 (1977), 362-374. MR 0469843, 10.1017/S1446788700020383 |
| Reference:
|
[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 |
| . |
