Semilatice Decompositions of Semigroups. Hereditariness and Periodicity—An Overview

  • Melanija MitrovićEmail author
  • Sergei Silvestrov
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 317)


A semigroup is an algebraic structure consisting of a set with an associative binary operation defined on it. We can say that most of the work within theory is done on semigroups with a finiteness condition, i.e. a semigroups possessing any property which is valid for all finite semigroups—like, for example, completely \(\pi \)-regularity, periodicity are. There are many different techniques for describing various kinds of semigroups. Among the methods with general applications is a semilattice decomposition of semigroups. Here, we are interested, in particular, in the decomposability of a certain type of semigroups with finiteness conditions into a semilattice of archimedean semigroups. Having in mind that the definition of finiteness condition may be given, also, in terms of elements of the semigroup, its subsemigroups, in terms of ideals or congruences of certain types, we choose to characterize them mostly by making connections between their elements and/or their special subsets. We are, also, going to list some of the applications of presented classes of semigroups and their semilattice decompositions in certain types of ring constructions. This overview, which is, by no mean, comprehensive one, is mainly based on the results presented in the book [27], and articles [8, 28, 29].


Semigroups Semilattices of archimedean semigroups MBC-semigroups GVS-semigroups Hereditary GVS-semigroups Periodic MBC-semigroups Combinatorial GVS-semigroups 

MSC 2010 Classification

06A12 20M05 20M15 20M17 20M18 16E60 



Melanija Mitrović is financially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Grant 174026, and by the Faculty of Mechanical Engineering, University of Niš, Serbia, Grant “Research and development of new generation machine systems in the function of the technological development of Serbia”. Melanija Mitrović is grateful to Mathematics and Applied Mathematics Research Environment MAM, Division of Applied Mathematics at the School of Education, Culture and Communication at Mälardalen University for cordial hospitality and excellent environment for research and cooperation during her visit.


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Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsFaculty of Mechanical Engineering, University of NišNišSerbia
  2. 2.Division of Applied Mathematics, School of EducationCulture and Communication, Mälardalen UniversityVästeråsSweden

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