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

1. Lipscomb S. L. The alternating semigroups: generators and congruences / S. L. Lipscomb // Semigroup Forum. — 1992. —
V. 44. — P. 96—106.
2. Derech V. D. On one class of factorizable fundamental inverse monoids / V. D. Derech // Ukr. Mat. Zh. — 2013. — V. 65,
№ 6. — P. 864—871.
3. Derech V. D. Stable quasi-orders on some permutable inverse monoids / V. D. Derech // Ukr. Mat. Zh. — 2014. — V. 66,
№ 4. — P. 445—457.
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.

Downloads

Abstract views: 121

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

Metrics

Downloads

Download data is not yet available.

License

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).