Affiliation:
1. Department of Algebra and System Analysis, Luhansk Taras Shevchenko National University, Gogol Square, 1, Starobilsk 92703, Ukraine
Abstract
Jean-Louis Loday and María O. Ronco introduced the notion of a trioid and constructed a free trioid of rank 1. In this paper, we give a survey of results on trioids. Different examples of trioids and new trioid theoretical constructions are given, combinatorial properties of operations on trioids are studied and some congruences on trioids are characterized. We also introduce the notion of a triband of subtrioids and in terms of tribands of subtrioids describe the structure of trioids. Moreover, we describe a free trioid of an arbitrary rank and for this trioid give an isomorphic construction. In addition, we introduce and study the notion of a semiretraction of a trioid and give some applications of semiretractions to the study of congruences on trioids. The main references are the papers by J.-L. Loday and M. O. Ronco as well as the author.
Publisher
World Scientific Pub Co Pte Lt
Reference48 articles.
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4. A. Clifford and G. Preston, The Algebraic Theory of Semigroups, Vols. 1 and 2 (Mir, 1972), p. 185, p. 422 (in Russian).
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