Multiplicatively idempotent semirings
Ivan Chajda; Helmut Länger; Filip Švrček
Mathematica Bohemica (2015)
- Volume: 140, Issue: 1, page 35-42
- ISSN: 0862-7959
Access Full Article
top
Abstract
topHow to cite
topChajda, Ivan, Länger, Helmut, and Švrček, Filip. "Multiplicatively idempotent semirings." Mathematica Bohemica 140.1 (2015): 35-42. <http://eudml.org/doc/269881>.
@article{Chajda2015,
abstract = {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.},
author = {Chajda, Ivan, Länger, Helmut, Švrček, Filip},
journal = {Mathematica Bohemica},
keywords = {semiring; commutative semiring; multiplicatively idempotent semiring; semiring of characteristic 2; simple semiring; unitary Boolean ring; bounded distributive lattice},
language = {eng},
number = {1},
pages = {35-42},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Multiplicatively idempotent semirings},
url = {http://eudml.org/doc/269881},
volume = {140},
year = {2015},
}
TY - JOUR
AU - Chajda, Ivan
AU - Länger, Helmut
AU - Švrček, Filip
TI - Multiplicatively idempotent semirings
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 1
SP - 35
EP - 42
AB - 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.
LA - eng
KW - semiring; commutative semiring; multiplicatively idempotent semiring; semiring of characteristic 2; simple semiring; unitary Boolean ring; bounded distributive lattice
UR - http://eudml.org/doc/269881
ER -
References
top- 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. (2012) Zbl1321.06011MR2908430
- Chajda, I., Švrček, F., 10.7151/dmgaa.1181, Discuss. Math., Gen. Algebra Appl. 31 (2011), 175-184. (2011) Zbl1262.06005MR2953910DOI10.7151/dmgaa.1181
- Clouse, D. J., Guzmán, F., 10.1007/s00012-011-0102-y, Algebra Univers. 64 (2010), 231-249. (2010) Zbl1217.06007MR2781078DOI10.1007/s00012-011-0102-y
- Golan, J. S., Semirings and Affine Equations over Them: Theory and Applications, Mathematics and Its Applications 556 Kluwer Academic Publishers, Dordrecht (2003). (2003) Zbl1042.16038MR1997126
- Golan, J. S., Semirings and Their Applications, Kluwer Academic Publishers Dordrecht (1999). (1999) Zbl0947.16034MR1746739
- Grätzer, G., Lakser, H., Płonka, J., 10.4153/CMB-1969-095-x, Can. Math. Bull. 12 (1969), 741-744. (1969) Zbl0188.04903MR0276160DOI10.4153/CMB-1969-095-x
- Guzmán, F., 10.1016/0022-4049(92)90108-R, J. Pure Appl. Algebra 78 (1992), 253-270. (1992) Zbl0770.16020MR1163278DOI10.1016/0022-4049(92)90108-R
- Jedlička, P., The rings which are Boolean, Part II, Acta Univ. Carol., Math. Phys. 53 (2012), 73-75. (2012) MR3099402
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.