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Finitely generated algebraic structures with various divisibility conditions
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Jaroslav Ježek
,
Vítězslav Kala
Published/Copyright:
February 25, 2012
Abstract.
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
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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Articles in the same Issue
- Masthead
- Uniform weighted estimates for oscillatory singular integrals
- Solutions of the linear Boltzmann equation and some Dirichlet series
- Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
- Periodic flat resolutions and periodicity in group (co)homology
- Precompact noncompact reflexive Abelian groups
-
Free profinite
-
Cellular covers for
- Time changes of local Dirichlet spaces by energy measures of harmonic functions
- A construction of a universal connection
- Finitely generated algebraic structures with various divisibility conditions
- Quasiprojective varieties admitting Zariski dense entire holomorphic curves
- Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
