Natalia Mazurenko | Searcharxiv

arXiv2026

On certain classes of commutative g-dimonoids

We study g-dimonoids, which are algebraic structures equipped with two associative binary operations satisfying a prescribed system of axioms. We develop a construction of g-dimonoids based on inflations of semigroups, construct several classes of 2-dinilpotent commutative g-dimonoids, and investigate the isomorphism problem for these classes. As an application of these results, we obtain a structural description of all commutative g-dimonoids of order 3, up to isomorphism.

math.GR↗

arXiv2026

Invariant idempotent $\ast$-measures for generalized iterated function systems

The notion of $\ast$-measure on a compact Hausdorff space can be defined for arbitrary continuous triangular norm $\ast$. The well-known Hutchinson-Barnsley theory deals with the iterated function systems (IFSs) of probability measures and establishes existence and uniqueness of invariant measures. In the previous paper, IFSs of $\ast$-measures were considered. In the present paper we deal with generalized invariant function systems (GIFSs) of $\ast$-measures, which are counterparts of GIFSs in the sense of Mihail and Miculescu. The notion of invariant $\ast$-measure is introduced for such GIFSs and we prove existence and uniqueness of such elements.

math.GN↗