Notes on commutative parasemifields

Kala, Vítězslav, Kepka, Tomáš, and Korbelář, Miroslav. "Notes on commutative parasemifields." Commentationes Mathematicae Universitatis Carolinae 50.4 (2009): 521-533. <http://eudml.org/doc/35127>.

@article{Kala2009,
abstract = {Parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) are considered in more detail. We show that if a parasemifield $S$ contains $\mathbb \{Q\}^+$ as a subparasemifield and is generated by $\mathbb \{Q\}^\{+\}\cup \lbrace a\rbrace $, $a\in S$, as a semiring, then $S$ is (as a semiring) not finitely generated.},
author = {Kala, Vítězslav, Kepka, Tomáš, Korbelář, Miroslav},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {semiring; ideal-simple; parasemifield; finitely generated; commutative semirings; ideal-simple semirings; finitely generated parasemifields},
language = {eng},
number = {4},
pages = {521-533},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Notes on commutative parasemifields},
url = {http://eudml.org/doc/35127},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Kala, Vítězslav
AU - Kepka, Tomáš
AU - Korbelář, Miroslav
TI - Notes on commutative parasemifields
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 4
SP - 521
EP - 533
AB - Parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) are considered in more detail. We show that if a parasemifield $S$ contains $\mathbb {Q}^+$ as a subparasemifield and is generated by $\mathbb {Q}^{+}\cup \lbrace a\rbrace $, $a\in S$, as a semiring, then $S$ is (as a semiring) not finitely generated.
LA - eng
KW - semiring; ideal-simple; parasemifield; finitely generated; commutative semirings; ideal-simple semirings; finitely generated parasemifields
UR - http://eudml.org/doc/35127
ER -