Скінченні локальні майже-кільця

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dc.contributor.authorРаєвська, Ірина
dc.contributor.authorРаєвська, Марина
dc.date.accessioned2018-12-13T15:13:20Z
dc.date.available2018-12-13T15:13:20Z
dc.date.issued2018
dc.description.abstractУ 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.abstractNearrings 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.identifier.citationРаєвська 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.issn2617-7080
dc.identifier.urihttps://ekmair.ukma.edu.ua/handle/123456789/14912
dc.identifier.urihttps://doi.org/10.18523/2617-7080i2018p38-48
dc.language.isoukuk_UA
dc.relation.sourceМогилянський математичний журнал : науковий журнал. - 2018. - Т. 1uk_UA
dc.statusfirst publisheduk_UA
dc.subjectлокальне майже-кiльцеuk_UA
dc.subjectмайже-кiльце з одиницеюuk_UA
dc.subjectадитивна групаuk_UA
dc.subjectмультиплiкативна групаuk_UA
dc.subjectстаттяuk_UA
dc.subjectlocal nearringen_US
dc.subjectnearring with identityen_US
dc.subjectadditive groupen_US
dc.subjectmultiplicative groupen_US
dc.titleСкінченні локальні майже-кільцяuk_UA
dc.title.alternativeFinite local nearringsen_US
dc.typeArticleuk_UA
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