Concerning one inverse semigroup related to the group of affine transformations of the field F5

Authors

  • A. A. Barkovska Vinnytsia National Technical University
  • V. D. Derech Vinnytsia National Technical University

Keywords:

група, інверсна напівгрупа, афінне перетворення, поле

Abstract

Let AF5 be a group of affine transformations of the field . The set of all injections, each of which is included in some affine transformations with respect to the usual operations of composition of binary relations forming inverse semigroup, which we denoted by I(AF5) in this paper we study various properties of semigroup I(AF5) In particular, we describes the group of automorphisms and congruency on I(AF5) Also we give answers to some combinatorial questions.

Author Biographies

A. A. Barkovska, Vinnytsia National Technical University

Senior Lecturer of the Chair of Higher Mathematics

V. D. Derech, Vinnytsia National Technical University

Cand. Sc. (Ph.-Math.), Assistant Professor, Assistant Professor of the Chair of Higher Mathematics

References

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3. Derech V. D. Stable quasi-orders on some permutable inverse monoids / V. D. Derech // Ukr. Mat. Zh. — 2014. — V. 66,
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4. Клиффорд А. Алгебраическая теория полугрупп / А. Клиффорд, Г. Престон. — М. : Мир, 1972, — Т. 1. — 286 с. —
Т. 2. — 422 с.
5. Hamilton H. Permutability of congruences on commutative semigroups / H. Hamilton // Semigroup Forum. — 1975. — V. 10.
— P. 55—66.
6. Derech V. D. Congruences of a permutable inverse semigroups of finite rank / V. D. Derech // Ukr. Mat. Zh. — 2005. —
V. 57, № 4. — P. 565—570.

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How to Cite

[1]
A. A. Barkovska and V. D. Derech, “Concerning one inverse semigroup related to the group of affine transformations of the field F5”, Вісник ВПІ, no. 5, pp. 155–160, Oct. 2014.

Issue

No 5 (2014)

Section

Strategy, content and new technologies of traning specialists at higher education institutions

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