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weakly associative lattice ring; weakly associative lattice group; representable wal-ring
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.
[1] A.  Bigard, K. Keimel and S. Wolfenstein: Groupes et anneaux réticulés. Springer Verlag, Berlin-Heidelberg-New York, 1977. MR 0552653
[2] S. Burris and H. P. Sankappanavar: A Course in Universal Algebra. Springer-Verlag, New York-Heidelberg-Berlin, 1981. MR 0648287
[3] E.  Fried: Tournaments and non-associative lattices. Ann. Univ. Sci. Budapest, Sect. Math. 13 (1970), 151–164. MR 0321837
[4] L. Fuchs: Partially Ordered Algebraic Systems. Mir, Moscow, 1965. (Russian) MR 0218283
[5] V. M.  Kopytov: Lattice Ordered Groups. Nauka, Moscow, 1984. (Russian) MR 0806956 | Zbl 0567.06011
[6] V. M. Kopytov, N. Ya.  Medvedev: The Theory of Lattice Ordered Groups. Kluwer Acad. Publ., Dordrecht, 1994. MR 1369091
[7] A. G.  Kurosch,: Lectures on General Algebra. Academia, Praha, 1977. (Czech)
[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
[9] J.  Rachůnek: Circular totally semi-ordered groups. Acta Univ. Palack. Olom. Fac. Rerum Natur. 114, Math. 33 (1994), 109–116. MR 1385751
[10] J.  Rachůnek: On some varieties of weakly associative lattice groups. Czechoslovak Math. J. 46 (121) (1996), 231–240. MR 1388612
[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
[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
[13] D.  Šalounová: Weakly associative lattice rings. Acta Math. Inform. Univ. Ostraviensis 8 (2000), 75–87. MR 1800224
[14] H.  Skala: Trellis theory. Algebra Universalis  1 (1971), 218–233. DOI 10.1007/BF02944982 | MR 0302523 | Zbl 0242.06003
[15] H.  Skala: Trellis Theory. Memoirs AMS, Providence, 1972. MR 0325474 | Zbl 0242.06004
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