| Title:
|
Characterizations of the $0$-distributive semilattice (English) |
| Author:
|
Balasubramani, P. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
237-252 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The $0$-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for $0$-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient. (English) |
| Keyword:
|
semilattice |
| Keyword:
|
prime ideal |
| Keyword:
|
filter |
| MSC:
|
06A12 |
| MSC:
|
06A99 |
| MSC:
|
06B10 |
| MSC:
|
06B99 |
| idZBL:
|
Zbl 1052.06002 |
| idMR:
|
MR2012602 |
| DOI:
|
10.21136/MB.2003.134177 |
| . |
| Date available:
|
2009-09-24T22:09:19Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134177 |
| . |
| Reference:
|
[1] P. Balasubramani, P. V. Venkatanarasimhan: Characterizations of the $0$-distributive lattice.J. Pure Appl. Math. 32 (2001), 315–324. MR 1826759 |
| Reference:
|
[2] G. Grätzer: Lattice Theory First Concepts and Distributive Lattices.W. H. Freeman, San Francisco, 1971. MR 0321817 |
| Reference:
|
[3] C. Jayaram: Prime $\alpha $-ideals in a $0$-distributive lattice.J. Pure Appl. Math. 17 (1986), 331–337. Zbl 0595.06010, MR 0835346 |
| Reference:
|
[4] Y. S. Pawar, N. K. Thakare: $0$-distributive semilattices.Canad. Math. Bull. 21 (1978), 469–475. MR 0523589, 10.4153/CMB-1978-080-6 |
| Reference:
|
[5] Y. S. Pawar, N. K. Thakare: Minimal prime ideals in $0$-distributive lattices.Period. Math. Hungar. 13 (1982), 237–246. MR 0683850, 10.1007/BF01847920 |
| Reference:
|
[6] G. Szasz: Introduction to Lattice Theory.Academic Press, New York, 1963. MR 0166118 |
| Reference:
|
[7] J. Varlet: A generalization of the notion of pseudocomplementedness.Bull. Soc. Roy. Sci. Liege 37 (1968), 149–158. MR 0228390 |
| Reference:
|
[8] J. Varlet: Distributive semilattices and Boolean lattices.Bull. Soc. Roy. Liege 41 (1972), 5–10. Zbl 0237.06011, MR 0307991 |
| Reference:
|
[9] P. V. Venkatanarasimhan: Pseudocomplements in posets.Proc. Amer. Math. Soc. 28 (1971), 9–17. MR 0272687, 10.1090/S0002-9939-1971-0272687-X |
| Reference:
|
[10] P. V. Venkatanarasimhan: Semiideals in semilattices.Col. Math. 30 (1974), 203–212. |
| . |