Скінченні локальні майже-кільця

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dc.contributor.author Раєвська, Ірина
dc.contributor.author Раєвська, Марина
dc.date.accessioned 2018-12-13T15:13:20Z
dc.date.available 2018-12-13T15:13:20Z
dc.date.issued 2018
dc.identifier.citation Раєвська І. Ю. Скінченні локальні майже-кільця / Раєвська І. Ю., Раєвська М. Ю. // Могилянський математичний журнал : науковий журнал. - 2018. - Т. 1. - С. 38-48. uk_UA
dc.identifier.issn 2617-7080
dc.identifier.uri http://ekmair.ukma.edu.ua/handle/123456789/14912
dc.identifier.uri https://doi.org/10.18523/2617-7080i2018p38-48
dc.description.abstract У статтi здiйснено огляд сучасного стану дослiдження скiнченних локальних майже-кiлець, а саме їх похiдних структур - адитивної та мультиплiкативної груп. Наведено класифiкацiю локальних майже-кiлець, порядок яких не перевищує 32. uk_UA
dc.description.abstract Nearrings arise naturally in the study of systems of nonlinear mappings, and they have been studied for many decades. Basic definitions and many results concerning nearrings can be, for instance, found in [G. Pilz. Near-rings. The theory and its applications. North Holland, Amsterdam, 1977]. Nearrings are generalized rings in the sense that the addition need not be commutative and only one distributive law is assumed. Clearly, every associative ring is a nearring, and each group is an additive group of a nearring, but not necessarily of a nearring with identity. The question what group can be an additive group of a nearring with identity is far from solution. A nearring with identity is called local if the set of all its non-invertible elements is a subgroup of its additive group. A study of local nearrings was initiated by Maxson (1968) who defined a number of their basic properties and proved, in particular, that the additive group of a finite zero-symmetric local nearring is a p-group. The determination of the non-abelian finite p-groups which are the additive groups of local nearrings is an open problem (Feigelstock, 2006). The list of all local nearrings of order at most 31 can be extracted from the package SONATA (https://www.gap-system.org/Packages/sonata.html) of the computer system algebra GAP (https:// www.gap-system.org/). We observe also that there exist 14 non-isomorphic groups of order 16 = 24 from which 9 are the additive groups of local nearrings. Groups of order 32 = 25 with this property are described. In particular, among 51 non-isomorphic groups of this order only 19 are these additive groups. In this paper finite local nearrings are studied. Moreover, local nearrings of order at most 32 are classified. en_US
dc.language.iso uk uk_UA
dc.subject локальне майже-кiльце uk_UA
dc.subject майже-кiльце з одиницею uk_UA
dc.subject адитивна група uk_UA
dc.subject мультиплiкативна група uk_UA
dc.subject стаття uk_UA
dc.subject local nearring en_US
dc.subject nearring with identity en_US
dc.subject additive group en_US
dc.subject multiplicative group en_US
dc.title Скінченні локальні майже-кільця uk_UA
dc.title.alternative Finite local nearrings en_US
dc.type Article uk_UA
dc.status first published uk_UA
dc.relation.source Могилянський математичний журнал : науковий журнал. - 2018. - Т. 1 uk_UA

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