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- Mitrovic, Melanija, et al.
(författare)
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Constructive Semigroups with Apartness : Towards a New Algebraic Theory
- 2019
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Ingår i: Journal of Physics, Conference Series. - : Institute of Physics Publishing (IOPP). - 1742-6588 .- 1742-6596. ; 1194:1, s. 1-8
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Tidskriftsartikel (refereegranskat)abstract
- The theory of constructive semigroups with apartness is a new approach tosemigroup theory, and not a new class of semigroups. Of course, our work is partly inspired byclassical semigroup theory, but, on the other hand, it is distinguished from it by two signicantaspects: rst, we use intuitionistic logic rather than classical, secondly, our work is based onthe notion of apartness (between elements, elements and sets). Here, the focus is on E. Bishop'sapproach to constructive mathematics (BISH)
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| 2. |
- Mitrović, Melanija, et al.
(författare)
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Isomorphism theorems for basic constructive algebraic structures with special emphasize on constructive semigroups with apartness—an overview
- 2020
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Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 653-686
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Bokkapitel (refereegranskat)abstract
- This overview is an introduction to the basic constructive algebraic structures with apartness with special emphasises on a set and semigroup with apartness. The main purpose of this paper, inspired by Bauer [2], is to make some sort of understanding of constructive algebra in Bishop’s style position for those (classical) algebraists as well as for the ones who apply algebraic knowledge who might wonder what is constructive algebra all about. Every effort has been made to produce a reasonably prepared text with such definite need. In the context of basic constructive algebraic structures constructive analogous of isomorphism theorems will be given. Following their development, two points of view on a given subject: classical and constructive will be considered. This overview is not, of course, a comprehensive one.
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| 3. |
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| 4. |
- Mitrović, Melanija, et al.
(författare)
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Semilatice decompositions of semigroups. Hereditariness and periodicity—An overview
- 2020
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Ingår i: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 687-721
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Bokkapitel (refereegranskat)abstract
- 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 π-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].
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