| Title:
|
Multiplicatively idempotent semirings (English) |
| Author:
|
Chajda, Ivan |
| Author:
|
Länger, Helmut |
| Author:
|
Švrček, Filip |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
140 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
35-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Semirings are modifications of unitary rings where the additive reduct does not form a group in general, but only a monoid. We characterize multiplicatively idempotent semirings and Boolean rings as semirings satisfying particular identities. Further, we work with varieties of enriched semirings. We show that the variety of enriched multiplicatively idempotent semirings differs from the join of the variety of enriched unitary Boolean rings and the variety of enriched bounded distributive lattices. We get a characterization of this join. (English) |
| Keyword:
|
semiring |
| Keyword:
|
commutative semiring |
| Keyword:
|
multiplicatively idempotent semiring |
| Keyword:
|
semiring of characteristic 2 |
| Keyword:
|
simple semiring |
| Keyword:
|
unitary Boolean ring |
| Keyword:
|
bounded distributive lattice |
| MSC:
|
06E20 |
| MSC:
|
16Y60 |
| idZBL:
|
Zbl 06433696 |
| idMR:
|
MR3324417 |
| DOI:
|
10.21136/MB.2015.144177 |
| . |
| Date available:
|
2015-03-09T17:37:57Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144177 |
| . |
| Reference:
|
[1] Chajda, I., Švrček, F.: Lattice-like structures derived from rings.Contributions to General Algebra 20, Proceedings of the 81st Workshop on General Algebra Salzburg, Austria Johannes Heyn Klagenfurt (2012), 11-18 J. Czermak et al. Zbl 1321.06011, MR 2908430 |
| Reference:
|
[2] Chajda, I., Švrček, F.: The rings which are Boolean.Discuss. Math., Gen. Algebra Appl. 31 (2011), 175-184. Zbl 1262.06005, MR 2953910, 10.7151/dmgaa.1181 |
| Reference:
|
[3] Clouse, D. J., Guzmán, F.: The dual geometry of Boolean semirings.Algebra Univers. 64 (2010), 231-249. Zbl 1217.06007, MR 2781078, 10.1007/s00012-011-0102-y |
| Reference:
|
[4] Golan, J. S.: Semirings and Affine Equations over Them: Theory and Applications.Mathematics and Its Applications 556 Kluwer Academic Publishers, Dordrecht (2003). Zbl 1042.16038, MR 1997126 |
| Reference:
|
[5] Golan, J. S.: Semirings and Their Applications.Kluwer Academic Publishers Dordrecht (1999). Zbl 0947.16034, MR 1746739 |
| Reference:
|
[6] Grätzer, G., Lakser, H., Płonka, J.: Joins and direct products of equational classes.Can. Math. Bull. 12 (1969), 741-744. Zbl 0188.04903, MR 0276160, 10.4153/CMB-1969-095-x |
| Reference:
|
[7] Guzmán, F.: The variety of Boolean semirings.J. Pure Appl. Algebra 78 (1992), 253-270. Zbl 0770.16020, MR 1163278, 10.1016/0022-4049(92)90108-R |
| Reference:
|
[8] Jedlička, P.: The rings which are Boolean, Part II.Acta Univ. Carol., Math. Phys. 53 (2012), 73-75. MR 3099402 |
| . |
