| Title:
|
Non-transitive generalizations of subdirect products of linearly ordered rings (English) |
| Author:
|
Rachůnek, Jiří |
| Author:
|
Šalounová, Dana |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
591-603 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Weakly associative lattice rings (wal-rings) are non-transitive generalizations of lattice ordered rings (l-rings). As is known, the class of l-rings which are subdirect products of linearly ordered rings (i.e. the class of f-rings) plays an important role in the theory of l-rings. In the paper, the classes of wal-rings representable as subdirect products of to-rings and ao-rings (both being non-transitive generalizations of the class of f-rings) are characterized and the class of wal-rings having lattice ordered positive cones is described. Moreover, lexicographic products of weakly associative lattice groups are also studied here. (English) |
| Keyword:
|
weakly associative lattice ring |
| Keyword:
|
weakly associative lattice group |
| Keyword:
|
representable wal-ring |
| MSC:
|
06F15 |
| MSC:
|
06F25 |
| MSC:
|
13J25 |
| MSC:
|
16W80 |
| idZBL:
|
Zbl 1080.06032 |
| idMR:
|
MR2000055 |
| . |
| Date available:
|
2009-09-24T11:04:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127825 |
| . |
| Reference:
|
[1] A. Bigard, K. Keimel and S. Wolfenstein: Groupes et anneaux réticulés.Springer Verlag, Berlin-Heidelberg-New York, 1977. MR 0552653 |
| Reference:
|
[2] S. Burris and H. P. Sankappanavar: A Course in Universal Algebra.Springer-Verlag, New York-Heidelberg-Berlin, 1981. MR 0648287 |
| Reference:
|
[3] E. Fried: Tournaments and non-associative lattices.Ann. Univ. Sci. Budapest, Sect. Math. 13 (1970), 151–164. MR 0321837 |
| Reference:
|
[4] L. Fuchs: Partially Ordered Algebraic Systems.Mir, Moscow, 1965. (Russian) MR 0218283 |
| Reference:
|
[5] V. M. Kopytov: Lattice Ordered Groups.Nauka, Moscow, 1984. (Russian) Zbl 0567.06011, MR 0806956 |
| Reference:
|
[6] V. M. Kopytov, N. Ya. Medvedev: The Theory of Lattice Ordered Groups.Kluwer Acad. Publ., Dordrecht, 1994. MR 1369091 |
| Reference:
|
[7] A. G. Kurosch,: Lectures on General Algebra.Academia, Praha, 1977. (Czech) |
| Reference:
|
[8] J. Rachůnek: Solid subgroups of weakly associative lattice groups.Acta Univ. Palack. Olom. Fac. Rerum Natur. 105, Math. 31 (1992), 13–24. MR 1212601 |
| Reference:
|
[9] J. Rachůnek: Circular totally semi-ordered groups.Acta Univ. Palack. Olom. Fac. Rerum Natur. 114, Math. 33 (1994), 109–116. MR 1385751 |
| Reference:
|
[10] J. Rachůnek: On some varieties of weakly associative lattice groups.Czechoslovak Math. J. 46 (121) (1996), 231–240. MR 1388612 |
| Reference:
|
[11] J. Rachůnek: A weakly associative generalization of the variety of representable lattice ordered groups.Acta Univ. Palack. Olom. Fac. Rerum Natur., Math. 37 (1998), 107–112. MR 1690479 |
| Reference:
|
[12] J. Rachůnek: Weakly associative lattice groups with lattice ordered positive cones.In: Contrib. Gen. Alg. 11, Verlag Johannes Heyn, Klagenfurt, 1999, pp. 173–180. MR 1696670 |
| Reference:
|
[13] D. Šalounová: Weakly associative lattice rings.Acta Math. Inform. Univ. Ostraviensis 8 (2000), 75–87. MR 1800224 |
| Reference:
|
[14] H. Skala: Trellis theory.Algebra Universalis 1 (1971), 218–233. Zbl 0242.06003, MR 0302523, 10.1007/BF02944982 |
| Reference:
|
[15] H. Skala: Trellis Theory.Memoirs AMS, Providence, 1972. Zbl 0242.06004, MR 0325474 |
| . |
