# Finite generation of congruence preserving functions

@article{Aichinger2015FiniteGO, title={Finite generation of congruence preserving functions}, author={Erhard Aichinger and Marijana Lazic and Nebojsa Mudrinski}, journal={Monatshefte f{\"u}r Mathematik}, year={2015}, volume={181}, pages={35-62} }

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.

## 6 Citations

Congruence preserving expansions of nilpotent algebras

- Mathematics, Computer ScienceInt. J. Algebra Comput.
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Those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruent expansions are characterized.

Rings of congruence preserving functions, II

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Abstract For several classes of special p-groups G, of exponent p, p > 2, we show that the near-ring, of congruence preserving functions on G is a ring if and only if G is a 1-affine complete group.

Rings of congruence preserving functions

- Mathematics, MedicineMonatshefte fur Mathematik
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This work investigates the question “When is C_0 (G)$$C0(G) a ring?” and obtains information externally via the lattice structure of the normal subgroups of G and internally via structural properties of the group G.

Congruence lattices forcing nilpotency

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Given a lattice $\mathbb{L}$ and a class $K$ of algebraic structures, we say that $\mathbb{L}$ \emph{forces nilpotency} in $K$ if every algebra $\mathbf{A} \in K$ whose congruence lattice…

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- MathematicsAlgebra universalis
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Specialized from lattice theory to the lattice of ideals of an expanded group, the equivalence relation of projectivity between two intervals of ideals I[A, B] and I[C, D] of an expanded group V…

The Weak Descending Chain Condition on Right Ideals for Nearrings

- 2019

The purpose of this paper is to introduce a weaker form of the descending chain condition on right ideals than the standard one. We shall see that fundamental results about socle and Frattini series…

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