$\mathcal{R}$-cross-sections 
of the semigroup $\mathcal{T}_X$ (in Ukrainian)

V. O. Pyekhtyeryev

1. Renner L.E. Analogue of Bruhat decomposition for algebraic monoids. II. The length function and the trichotomy// J. Algebra . – 1995. – V. 175, № 2. – P.697–714.

2. Cowan D.F., Reily R. Partial cross-sections of symmetric inverse semigroups// Internat J. Algebra Comput. – 1995. – V.5, № 3. – P.259–287.

3. Ganyushkin O., Mazorchuk V. $\mathcal{L}$- and $\mathcal{R}$-cross-sections in $IS_n$// Com. in Algebra. -- 2003. -- V.31, № 9. -- P.4507--4523.

4. Клифорд А., Престон Г. Алгебраическая теория полугрупп. Т.1,2. – М.: Мир, 1972.

5. Pyekhtyeryev V. $\mathcal{H}$- and $\mathcal{R}$-cross-sections of the full finite semigroup $T_n$ // J. Algebra and Discrete Mathematics.\ -- 2003.\ -- № 3.\ -- P.82--88.

	$\mathcal{R}$-cross-sections of the semigroup $\mathcal{T}_X$ (in Ukrainian)
Author	V. O. Pyekhtyeryev vasiliy@univ.kiev.ua Taras Shevcnehno Kyiv National University
Abstract	We classify cross-sections of the $\mathcal{R}$ Green relation on the full semigroup $\mathcal{T}_X$ and determine which of them are isomorphic.
Keywords	Green relation, full semigroup, cross-section
DOI	doi:10.30970/ms.21.2.133-139
Reference	1. Renner L.E. Analogue of Bruhat decomposition for algebraic monoids. II. The length function and the trichotomy// J. Algebra . – 1995. – V. 175, № 2. – P.697–714. 2. Cowan D.F., Reily R. Partial cross-sections of symmetric inverse semigroups// Internat J. Algebra Comput. – 1995. – V.5, № 3. – P.259–287. 3. Ganyushkin O., Mazorchuk V. $\mathcal{L}$- and $\mathcal{R}$-cross-sections in $IS_n$// Com. in Algebra. -- 2003. -- V.31, № 9. -- P.4507--4523. 4. Клифорд А., Престон Г. Алгебраическая теория полугрупп. Т.1,2. – М.: Мир, 1972. 5. Pyekhtyeryev V. $\mathcal{H}$- and $\mathcal{R}$-cross-sections of the full finite semigroup $T_n$ // J. Algebra and Discrete Mathematics.\ -- 2003.\ -- № 3.\ -- P.82--88.
Pages	133-139
Volume	21
Issue	2
Year	2004
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

$\mathcal{R}$-cross-sections of the semigroup $\mathcal{T}_X$ (in Ukrainian)