A note on Stone join-semilattices

• Autorzy: Shriram Nimbhorkar , Anwari Rahemani
• Języki publikacji: EN

Abstrakty

EN

Characterizations for a pseudocomplemented modular join-semilattice with 0 and 1 and its ideal lattice to be a Stone lattice are given.

Słowa kluczowe

EN

Pseudocomplemented lattice; Stone lattice; Modular join-semilattice

Kategorie tematyczne

• 06D99: None of the above, but in this section
• 06A06: Partial order, general

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 4
• Strony: 929-933

Daty

wydano

2011-08-01

online

2011-05-26

Twórcy

autor

Shriram Nimbhorkar

• Dr. Babasaheb Ambedkar Marathwada University

autor

Anwari Rahemani

• Dr. Babasaheb Ambedkar Marathwada University

Bibliografia

• [1] Balbes R., Horn A., Stone lattices, Duke Math. J., 1970, 37(3), 537–545 http://dx.doi.org/10.1215/S0012-7094-70-03768-3
• [2] Birkhoff G., Lattice Theory, 2nd ed., Amer. Math. Soc. Colloq. Publ., 25, American Mathematical Society, New York, 1948
• [3] Frink O., Pseudo-complements in semi-lattices, Duke Math. J., 1962, 29(4), 505–514 http://dx.doi.org/10.1215/S0012-7094-62-02951-4
• [4] Grätzer G., A generalization of Stone’s representation theorem for Boolean algebras, Duke Math. J., 1963, 30(3), 469–474 http://dx.doi.org/10.1215/S0012-7094-63-03051-5
• [5] Grätzer G., Lattice Theory: First concepts and Distributive Lattices, W. H. Freemanand Co., San Francisco, 1971
• [6] Grätzer G., Schmidt E. T., On a problem of M. H. Stone, Acta Math. Acad. Sci. Hungar., 1957, 8(3–4), 455–460 http://dx.doi.org/10.1007/BF02020328
• [7] Katriňák T., Mederly P., Construction of p-algebras with a modular frame, Houston J. Math., 1978, 4(1), 67–79
• [8] Stone M. H., Topological representations of distributive lattices and Brouwerian logics, Časopis Pěst. Mat. Fys., 1937, 67, 1–25
• [9] Varlet J., On the characterization of Stonelattices, Acta Sci. Math. (Szeged), 1966, 27(1–2), 81–84
• [10] Venkatanarasimhan P.V., A note on modular lattices, J. Indian Math. Soc., 1966, 30, 55–59
• [11] Venkatanarasimhan P.V., Pseudo-complements in posets, Proc. Amer. Math. Soc., 1971, 28(1), 9–17 http://dx.doi.org/10.1090/S0002-9939-1971-0272687-X

Identyfikatory

DOI

10.2478/s11533-011-0031-1