# Full and elementary nets over the field of fractions of a principal ideal ring : доклад, тезисы доклада

#### Описание

Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: Groups and Graphs, Metrics and Manifolds; Yekaterinburg; Yekaterinburg

Год издания: 2017

Аннотация: Let R be a commutative ring with unit and n be an integer. The set a = ), 1 < i, j < n, of additive subgroups of the ring R is called a net (carpet) under the ring R of the order n, if ajr arj С ajj- for all values of i, r, j An elementary net of order n over R [1-3] is a set of additive subgroups (without diagonal) a = (ajj-), 1 <Показать полностьюi = j < n R ajr arj С ajj, i = j, i = r, r = j, 1 < i, r, j. A net is called irreducible, if ajj- = 0 for all An example of an irreducible net is the net of constant aP, defined for an arbitrary non-zero ring P such that (aP= P for all i, j. Let K be a field of fractions of a principal ideal ring R, and a = (ajj-) be a full (elementary) net of order n > 2 (respectively, n > 3) over K ajj R ajj

#### Издание

Журнал: Groups and Graphs, Metrics and Manifolds

Номера страниц: 44-44

Издатель: Уральский федеральный университет имени первого Президента России Б.Н. Ельцина

#### Авторы

• Dryaeva Roksana Y (North Ossetian State University)
• Koibaev Vladimir A. (North Ossetian State University)
• Nuzhin Yakov N. (Siberian Federal University)
• Krasovskii Institute of Mathematics and Mechanics UB RAS Ural Federal University named after the first President of Russia B.N. Yeltsin