Papers by Erhard Aichinger
Archiv der Mathematik, 2011
Fried and MacRae (Math. Ann. 180, 220–226 (1969)) proved that for univariate polynomials $${p,q, ... more Fried and MacRae (Math. Ann. 180, 220–226 (1969)) proved that for univariate polynomials $${p,q, f, g \in \mathbb{K}[t]}$$ ($${\mathbb{K}}$$ a field) with p, q nonconstant, p(x) − q(y) divides f(x) − g(y) in $${\mathbb{K}[x,y]}$$ if and only if there is $${h \in \mathbb{K}[t]}$$ such that f = h(p(t)) and g = h(q(t)). Schicho (Arch. Math. 65, 239–243 (1995)) proved this theorem from the viewpoint
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Monatshefte für Mathematik, 2015
ABSTRACT We investigate when the clone of congruence preserving functions is finitely generated. ... more ABSTRACT We investigate when the clone of congruence preserving functions is finitely generated. We obtain a full description for all finite $p$-groups, and for all finite algebras with Mal'cev term and simple congruence lattice. The characterization for $p$-groups allows a generalization to a large class of expansions of groups.
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Publicationes Mathematicae Debrecen, 2013
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International Journal of Algebra and Computation, 2015
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ABSTRACT
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Classes of algebraic structures that are defined by equational laws are called varieties or equat... more Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every subvariety of a finitely generated congruence permutable variety is finitely generated; in fact, we prove the more general result that if a finitely generated variety has an edge term, then all its subvarieties are finitely generated as well. This applies in particular to all varieties of groups, loops, quasigroups and their expansions (e.g., modules, rings, Lie algebras,...).
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Proceedings of the 2000 international symposium on Symbolic and algebraic computation symbolic and algebraic computation - ISSAC '00, 2000
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Journal of the European Mathematical Society, 2014
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Rocky Mountain Journal of Mathematics, 2008
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Order, 2013
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Monatshefte für Mathematik, 2011
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Journal of Algebra, 2004
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Communications in Algebra, 2003
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Algebra universalis, 2009
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Acta Mathematica Hungarica, 2007
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Acta Mathematica Hungarica, 2010
ABSTRACT We show that the polynomials of every finite Mal’cev algebra with congruence lattice of ... more ABSTRACT We show that the polynomials of every finite Mal’cev algebra with congruence lattice of height at most 2 can be described by a finite set of relations. Key words and phrasescommutator theory-Mal’cev clone-polynomial completeness-polynomial function 2000 Mathematics Subject Classification08A40
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Aequationes Mathematicae, 2004
... (4.5) Therefore, the multiplication is completely determined by (4.1), (4.2), and (4.3) if we... more ... (4.5) Therefore, the multiplication is completely determined by (4.1), (4.2), and (4.3) if we define i◦(1+x∗i) for all x ∈ Zp. ... This implies (4.9), and hence ◦f is associative. The distributive law and zero-symmetric property can be verified by inspection of (4.8). ...
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Papers by Erhard Aichinger