| Title:
|
Weak pseudo-complementations on ADL’s (English) |
| Author:
|
Vasu Babu, R. |
| Author:
|
Santhi Sundar Raj, Ch. |
| Author:
|
Venkateswarlu, B. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
50 |
| Issue:
|
3 |
| Year:
|
2014 |
| Pages:
|
151-159 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
almost distributive lattice |
| Keyword:
|
Boolean algebra |
| Keyword:
|
Boolean ring |
| Keyword:
|
pseudo-complementation |
| Keyword:
|
weak pseudo-complementation |
| MSC:
|
06D99 |
| idZBL:
|
Zbl 1324.06016 |
| idMR:
|
MR3263657 |
| DOI:
|
10.5817/AM2014-3-151 |
| . |
| Date available:
|
2014-09-20T17:09:33Z |
| Last updated:
|
2016-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143923 |
| . |
| Reference:
|
[1] Birkhoff, G.: Lattice theory.American Mathematical Society Colloquium Publications, vol. XXV, American Mathematical Society, Providence, 1967. Zbl 0153.02501 |
| Reference:
|
[2] Frink, O.: Pseudo-complementes in semilattices.Duke Math. J. 29 (1961), 505–514. MR 0140449, 10.1215/S0012-7094-62-02951-4 |
| Reference:
|
[3] Lee, K.B.: Equational class of distributive pseudo-complemeneted lattice.Canadian J. Math. 22 (1970), 881–891. MR 0265240, 10.4153/CJM-1970-101-4 |
| Reference:
|
[4] Speed, T.P.: On Stone lattices.J. Australian Math. Soc. 9 (1967), 297–307. MR 0246801, 10.1017/S1446788700007217 |
| Reference:
|
[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. MR 2669039, 10.1142/S179355711000026X |
| Reference:
|
[6] Swamy, U.M., Rao, G.C.: Almost distributive lattices.J. Australian Math. Soc. 31 (1981), 77–91, (Series A). Zbl 0473.06008, MR 0622814, 10.1017/S1446788700018498 |
| Reference:
|
[7] Swamy, U.M., Rao, G.C., Rao, G.N.: Pseudo complementation on almost distributive lattices.Southeast Asian Bull. Math. 24 (2000), 95–104. Zbl 0982.06011, MR 1811218, 10.1007/s10012-000-0095-5 |
| Reference:
|
[8] Venkateswarlu, B., Vasu Babu, R.: Asssociate elements in ADL’s.Asian-Eur. J. Math. (to appear). |
| . |
