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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10127151%21RIV13-GA0-11320___
rdf:type
n4:Vysledek skos:Concept
rdfs:seeAlso
http://dx.doi.org/10.1515/FORM.2011.068
dcterms:description
Infinite fields are not finitely generated rings. A similar question is considered for further algebraic structures, mainly commutative semirings. In this case, purely algebraic methods fail and topological properties of integral lattice points turn out to be useful. We prove that a commutative setniring that is a group with respect to multiplication can be two-generated only if it belongs to the subclass of additively idempotent semirings; this class is equivalent to l-groups. Infinite fields are not finitely generated rings. A similar question is considered for further algebraic structures, mainly commutative semirings. In this case, purely algebraic methods fail and topological properties of integral lattice points turn out to be useful. We prove that a commutative setniring that is a group with respect to multiplication can be two-generated only if it belongs to the subclass of additively idempotent semirings; this class is equivalent to l-groups.
dcterms:title
Finitely generated algebraic structures with various divisibility conditions Finitely generated algebraic structures with various divisibility conditions
skos:prefLabel
Finitely generated algebraic structures with various divisibility conditions Finitely generated algebraic structures with various divisibility conditions
skos:notation
RIV/00216208:11320/12:10127151!RIV13-GA0-11320___
n4:predkladatel
n5:orjk%3A11320
n3:aktivita
n15:P
n3:aktivity
P(GA201/09/0296)
n3:cisloPeriodika
2
n3:dodaniDat
n19:2013
n3:domaciTvurceVysledku
n17:3441644 n17:6532713 n17:5613833
n3:druhVysledku
n9:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n16:predkladatel
n3:idSjednocenehoVysledku
136628
n3:idVysledku
RIV/00216208:11320/12:10127151
n3:jazykVysledku
n6:eng
n3:klicovaSlova
quasigroup; semiring; simple; Finitely generated
n3:klicoveSlovo
n10:simple n10:Finitely%20generated n10:quasigroup n10:semiring
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[E6FC06C8179C]
n3:nazevZdroje
Forum Mathematicum
n3:obor
n11:BA
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
3
n3:projekt
n14:GA201%2F09%2F0296
n3:rokUplatneniVysledku
n19:2012
n3:svazekPeriodika
24
n3:tvurceVysledku
Kala, Vítězslav Ježek, Jaroslav Kepka, Tomáš
n3:wos
000303419000010
s:issn
0933-7741
s:numberOfPages
19
n21:doi
10.1515/FORM.2011.068
n20:organizacniJednotka
11320