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Keywords:
almost distributive lattice; Boolean algebra; Boolean ring; pseudo-complementation; weak pseudo-complementation
Summary:
The notion of an Almost Distributive Lattice (abbreviated as ADL) was introduced by U. M. Swamy and G. C. Rao [6] as a common abstraction of several lattice theoretic and ring theoretic generalization of Boolean algebras and Boolean rings. In this paper, we introduce the concept of weak pseudo-complementation on ADL’s and discuss several properties of this.
References:
[1] Birkhoff, G.: Lattice theory. American Mathematical Society Colloquium Publications, vol. XXV, American Mathematical Society, Providence, 1967. Zbl 0153.02501
[2] Frink, O.: Pseudo-complementes in semilattices. Duke Math. J. 29 (1961), 505–514. DOI 10.1215/S0012-7094-62-02951-4 | MR 0140449
[3] Lee, K.B.: Equational class of distributive pseudo-complemeneted lattice. Canadian J. Math. 22 (1970), 881–891. DOI 10.4153/CJM-1970-101-4 | MR 0265240
[4] Speed, T.P.: On Stone lattices. J. Australian Math. Soc. 9 (1967), 297–307. DOI 10.1017/S1446788700007217 | MR 0246801
[5] Swamy, U.M., Ramesh, S., Sundar Raj, Ch.S.: Prime ideal characterizations of Stone ADL’s. Asian-Eur. J. Math. 3 (2010), no. 2, 357–367. DOI 10.1142/S179355711000026X | MR 2669039
[6] Swamy, U.M., Rao, G.C.: Almost distributive lattices. J. Australian Math. Soc. 31 (1981), 77–91, (Series A). DOI 10.1017/S1446788700018498 | MR 0622814 | Zbl 0473.06008
[7] Swamy, U.M., Rao, G.C., Rao, G.N.: Pseudo complementation on almost distributive lattices. Southeast Asian Bull. Math. 24 (2000), 95–104. DOI 10.1007/s10012-000-0095-5 | MR 1811218 | Zbl 0982.06011
[8] Venkateswarlu, B., Vasu Babu, R.: Asssociate elements in ADL’s. Asian-Eur. J. Math. (to appear).
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