| Title:
|
On a Construction of ModularGMS-algebras (English) |
| Author:
|
Badawy, Abd El-Mohsen |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
54 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
19-31 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety $\mathbf {\underline{K}}_{2}$ by means of $\underline{K}_{2}$-quadruples. We also characterize isomorphisms of these algebras by means of $\underline{K}_{2}$-quadruples. (English) |
| Keyword:
|
$\mathit {MS}$-algebras |
| Keyword:
|
$\mathit {GMS}$-algebras |
| Keyword:
|
$K_{2}$-algebras |
| Keyword:
|
Kleene algebras |
| Keyword:
|
isomorphisms |
| MSC:
|
06D05 |
| MSC:
|
06D30 |
| idZBL:
|
Zbl 1356.06008 |
| idMR:
|
MR3468598 |
| . |
| Date available:
|
2015-09-01T08:55:52Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144365 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Blyth, T. S., Varlet, J. C.: On a common abstraction of De Morgan algebras and Stone algebras. Proc. Roy. Soc. Edinburgh A 94 (1983), 301–308. Zbl 0536.06013, MR 0709723 |
| Reference:
|
[4] Blyth, T. S., Varlet, J. C.: Sur la construction de certaines MS-algèbres. Portugaliea Math. 39 (1980), 489–496. MR 0776258 |
| Reference:
|
[5] Blyth, T. S., Varlet, J. C.: Corrigendum “Sur la construction de certaines MS-algèbres”. Portugaliea Math. 42 (1983/84), 469–471. MR 0836125 |
| Reference:
|
[6] Chen, C. C., Grätzer, G.: Stone lattices I, Construction theorems. Canad. J. Math. 21 (1969), 884–894. Zbl 0184.03303, MR 0242737, 10.4153/CJM-1969-096-5 |
| Reference:
|
[7] Chen, C. C., Grätzer, G.: Stone lattices II, Structure theorems. Canad. J. Math. 21 (1969), 895–903. Zbl 0184.03304, MR 0242738, 10.4153/CJM-1969-097-2 |
| Reference:
|
[8] Haviar, M.: On a certain construction of MS-algebras. Portugliae Mathematica 51 (1994), 71–83. Zbl 0815.06011, MR 1281957 |
| Reference:
|
[9] Katriňák, T.: Die Konstruktion der distributiven pseudokomplementären verbande. Math. Nachrichten 53 (1972), 85–89. 10.1002/mana.19720530109 |
| Reference:
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[10] Katriňák, T., Mederly, P.: Construction of modular p-algebras. Algebra Univ. 4 (1974), 301–315. Zbl 0316.06005, MR 0354470, 10.1007/BF02485742 |
| Reference:
|
[11] Katriňák, T., Mikula, K.: On a construction of MS-algebeas. Portugliae Mathematica 45 (1978), 157–163. |
| Reference:
|
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| . |
