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Article

Joshi, Vinayak V. ; Waphare, B. N.
Characterizations of 0-distributive posets. (English). Mathematica Bohemica, vol. 130 (2005), issue 1, pp. 73-80
MSC: 06A06, 06A11, 06C15, 06C20, 06D15 | MR 2128360 | Zbl 1112.06001 | DOI: 10.21136/MB.2005.134222
Keywords:
0-distributive; pseudocomplement; sectionally semi-complemented poset; ideal lattice
Summary:
The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.
References:
[1] G. Grätzer: General Lattice Theory. Birkhäuser, New York, 1998. MR 1670580
[2] P. A. Grillet, J. C. Varlet: Complementedness conditions in lattices. Bull. Soc. Roy. Sci. Liège 36 (1967), 628–642. MR 0228389
[3] R. Halaš: Pseudocomplemented ordered sets. Arch. Math. (Brno) 29 (1993), 153–160. MR 1263116
[4] R. Halaš: Annihilators and ideals in distributive and modular ordered sets. Acta Univ. Palacki. Olomuc. Fac. Rerum Natur. Math. 34 (1995), 31–37. MR 1447252
[5] C. S. Hoo, K. P. Shum: $0$-Distributive and $P$-uniform semilattices. Canad. Math. Bull. 25 (1982), 317–324. DOI 10.4153/CMB-1982-044-1 | MR 0668948
[6] C. Jayaram: Complemented semilattices. Math. Semin. Notes, Kobe Univ. 8 (1980), 259–267. MR 0601893 | Zbl 0453.06005
[7] J. Larmerová, J. Rachůnek: Translations of distributive and modular ordered sets. Acta Univ. Palacki. Olomuc. Fac. Rerum Natur. Math. 27 (1988), 13–23. MR 1039879
[8] M. M. Pawar, B. N. Waphare: On Stone posets and strongly pseudocomplemented posets. J. Indian Math. Soc. (N.S.) 68 (2001), 91–95. MR 1929825
[9] Y. S. Pawar, V. B. Dhamke: 0-distributive posets. Indian J. Pure Appl. Math. 20 (1989), 804–811. MR 1012883
[10] Y. S. Pawar, N. K. Thakare: 0-distributive semilattices. Canad. Math. Bull. 21 (1978), 469–475. DOI 10.4153/CMB-1978-080-6 | MR 0523589
[11] J. C. Varlet: A generalization of the notion of pseudo-complementedness. Bull. Soc. Roy. Sci. Liège 37 (1968), 149–158. MR 0228390 | Zbl 0162.03501
[12] J. C. Varlet: Distributive semilattices and Boolean lattices. Bull. Soc. Roy. Sci. Liège 41 (1972), 5–10. MR 0307991 | Zbl 0237.06011
[13] P. V. Venkatanarasimhan: Pseudo-complements in posets. Proc. Amer. Math. Soc. 28 (1971), 9–17. DOI 10.1090/S0002-9939-1971-0272687-X | MR 0272687 | Zbl 0218.06002
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