Introduction to coalgebra.
Invariance groups of finite functions and orbit equivalence of permutation groups
Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections...
Invariants of the rational equivalence.
Inverse semirings and their lattice of congruences
Isomorphic algebraic pre-closures and equivalent set-systems
Isomorphisms of products of infinite connected graphs
Isotone analogs of results by Mal'tsev and Rosenberg.
Isotopy invariant quasigroup identities
According to S. Krstić, there are only four quadratic varieties which are closed under isotopy. We give a simple procedure generating quadratic identities and deciding which of the four varieties they define. There are about 37000 such identities with up to five variables.
Iterative nondeterministic algebras
Join-closed and meet-closed subsets in complete lattices
To every subset of a complete lattice we assign subsets , and define join-closed and meet-closed sets in . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.
Joins and meets of congruences on a regular semigroup.
Joins of congruences in -groups
k-ary monoids of term operations.
Kernels of tolerance relations.
k-Normalization and (k+1)-level inflation of varieties
Let τ be a type of algebras. A common measurement of the complexity of terms of type τ is the depth of a term. For k ≥ 1, an identity s ≈ t of type τ is said to be k-normal (with respect to this depth complexity measurement) if either s = t or both s and t have depth ≥ k. A variety is called k-normal if all its identities are k-normal. Taking k = 1 with respect to the usual depth valuation of terms gives the well-known property of normality of identities or varieties. For any variety V, there is...
Konstanten in endlichen, freien universellen Algebren.
Konzepte in den triadischen Kontext
Korrekturen zur Arbeit: Über die Existenz von freien Algebren. Math. Z. 106, 312 - 320 (1968).
La notion d'associativité relative
Large classes of functionally complete groupoids I.