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Keywords:
implicative ideals; modular ideals; pentagonal ideals; even ideals; rectangular ideals; medial ideals; modularity; distributivity
Summary:
This paper studies basic properties for five special types of implicative ideals (modular, pentagonal, even, rectangular and medial). The results are used to prove characterizations of modularity and distributivity.
References:
[1] Beran L.: On semiprime ideals in lattices. Journ. Pure Appl. Algebra 64 (1990), 223-227. MR 1061299 | Zbl 0703.06003
[2] Beran L.: Orthomodular Lattices (Algebraic Approach). Reidel Dordrecht (1985). MR 0784029 | Zbl 0558.06008
[3] Beran L., Salvati S.: Boolean algebras revisited. Boll. Unione Matem. Italiana, ser. VII, 9 (sez. B) (1997), 895-901. MR 1491733 | Zbl 0895.06007
[4] Rav Y.: Semiprime ideals in general lattices. Journ. Pure Appl. Algebra 56 (1989), 105-118. MR 0979666 | Zbl 0665.06006
[5] Salvati S.: A characterization of Boolean algebras. Ricerche di Matematica 43 (1994), 357-363. MR 1324757 | Zbl 0915.06005
[6] Zassenhaus H.: The Theory of Groups, (2nd ed.). Vandenhoeck & Ruprecht Göttingen (1958). MR 0091275 | Zbl 0083.24517
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