Results 11 to 20 of about 63 (57)

Mitschke’s theorem is sharp [PDF]

, 2022
Mitschke showed that a variety with an m-ary near-unanimity term has Jonsson terms t(0), ..., t(2m-4) witnessing congruence distributivity. We show that Mitschke's result is sharp.
Lipparini, Paolo
core   +1 more source

Day's Theorem is sharp for $n$ even

, 2022
We solve some problems about relative lengths of Maltsev conditions, in particular, we give an affirmative answer to a classical problem raised by A. Day more than fifty years ago.
Lipparini, Paolo
core   +2 more sources

The Tschantz and the alvin higher conditions are equivalent in congruence distributive varieties [PDF]

, 2020
We show that, under the assumption of congruence distributivity, a condition by S. Tschantz characterizing congruence modularity is equivalent to a variant of the classical Jonsson condition.
Lipparini, P
core   +1 more source

Congruence modularity implies cyclic terms for finite algebras [PDF]

, 2009
An n-ary operation f : A(n) -> A is called cyclic if it is idempotent and f(a(1), a(2), a(3), ... , a(n)) = f(a(2), a(3), ... , a(n), a(1)) for every a(1), ... , a(n) is an element of A.
McKenzie, Ralph, Maróti, Miklós, Kozik, Marcin, Barto, Libor, Niven, Todd   +4 more
core   +1 more source

The Jónsson distributivity spectrum [PDF]

, 2018
Suppose throughout that V is a congruence distributive variety. If m ≥ 1, let J V (m) be the smallest natural number k such that the congruence identity α(β ◦ γ ◦ β . . . ) ⊆ αβ ◦ αγ ◦ αβ ◦ . . .
Paolo Lipparini, Lipparini, Paolo, Lipparini, P   +2 more
core   +1 more source

Optimal Mal'tsev conditions for congruence modular varieties

, 2005
For varieties, congruence modularity is equivalent to the tolerance intersection property, TIP in short. Based on TIP, it was proved in [5] that for an arbitrary lattice identity implying modularity (or at least congruence modularity) there exists a Mal ...
Czedli, L, LIPPARINI, PAOLO, Horvath, EK
core   +1 more source

Tolerance distributive and tolerance modular varieties of commutative semigroups [PDF]

, 1986
summary:We present a formal scheme which whenever satisfied by relations of a given relational lattice $L$ containing only reflexive and transitive relations ensures distributivity of $L$
Chajda, Ivan, Chajda, I., Pondělíček, Bedřich   +2 more
core   +1 more source

On the degrees of permutability of subregular varieties [PDF]

, 1997
summary:An algebra ${\mathcal A}= (A,F)$ is subregular alias regular with respect to a unary term function $g$ if for each $\Theta , \Phi \in \text{Con}\,{\mathcal A}$ we have $\Theta = \Phi $ whenever $[g(a)]_{\Theta } = [g(a)]_{\Phi }$ for each $a\in A$
Raftery, James G., Ivan Chajda, Barbour, Graham D., Chajda, Ivan, James G. Raftery, Graham D. Barbour   +5 more
core   +1 more source

Congruence schemes and their applications [PDF]

, 2005
summary:Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority ...
S. Radeleczki, Chajda, I., I. Chajda, Radelecki, S.   +3 more
core  

On varieties of regular $*$-semigroups [PDF]

, 1991
summary:The paper contains characterizations of semigroup varieties whose semigroups with one generator (two generators) are permutable. Here all varieties of regular $*$-semigroups are described in which each semigroup with two generators is ...
Bedřich Pondělíček, Pondělíček, Bedřich   +1 more
core   +1 more source