Abstract
Two complete lattices, M and N, lying in an algebra over the field of rational numbers, are said to be weakly left equivalent if N=KM and M=¯KN, where K is a two-sided invertible lattice and ¯K is the inverse for K. In this paper we prove that the number of equivalence classes of lattices contained in a weak equivalence class is finite.
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D. K. Faddeev, “Introduction to the multiplicative theory of modules of integral representations,” Trudy Matem. Inst. Akad. Nauk SSSR,80, 145–182 (1965).
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I. A. Levina, “On the number of classes of exact ideals for Z-rings in a commutative Q-algebra,” Matem. Zametki,11, No. 4, 381–388 (1972).
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Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 501–508, March, 1974.
The author expresses his thanks to D. K. Faddeev for his interest in this work.
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Levina, I.A. Number of equivalence classes of weakly equivalent lattices. Mathematical Notes of the Academy of Sciences of the USSR 15, 292–295 (1974). https://doi.org/10.1007/BF01438386
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DOI: https://doi.org/10.1007/BF01438386