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Licensed Unlicensed Requires Authentication Published by De Gruyter February 25, 2012

Finitely generated algebraic structures with various divisibility conditions

  • Jaroslav Ježek EMAIL logo , Vítězslav Kala and Tomáš Kepka
From the journal Forum Mathematicum


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 semiring 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 -groups.

Received: 2009-10-15
Revised: 2010-03-12
Published Online: 2012-02-25
Published in Print: 2012-March

© 2012 by Walter de Gruyter Berlin Boston

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