Groups and noncommutative algebra: interactions and applications

Introduction to cyclic codes over commutative rings and algebraic integer numbers ...

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**Abstract**

We intend to continue the research on non commutative algebra. In particular, we wish to study the interactions between Group theory and the Theory of Rings and Algebras, as well as some of its applications, especially, to partial actions of groups on rings and to the Theory of Error-correcting Codes. Our group has worked on these directions for quite some time in the past and has already obtained results that are frequently quoted in the literature. Specific subjects to be studied in the period are, among others:* The structure of group algebras, considered as rings with involution and the group of units of a group ring.* The structure of the group of units of a division ring and the existence of free pairs of special type.* Study of globalization of partial actions, generalized crossed products, isomorphism of partial group algebras, partial actions and co-actions of Hopf algebras, partial projective representations and co-homology based on partial actions.* The study of error-correcting codes, defined from groups. In particular, we expect to study the relations among different classes of codes - cyclic, abelian, metacyclic, etc. - using techniques of finite group algebras. (AU)

Scientific publications
(17)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DOKUCHAEV, MIKHAILO;
KHRYPCHENKO, MYKOLA;
JACOBO SIMON, JUAN.
GLOBALIZATION OF PARTIAL COHOMOLOGY OF GROUPS.
** TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY**,
v. 374,
n. 3,
p. 1863-1898,
MAR 2021.
Web of Science Citations: 0.

SANCHEZ, JAVIER.
Free Group Algebras in Division Rings with Valuation II.
** CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES**,
v. 72,
n. 6,
p. 1463-1504,
DEC 2020.
Web of Science Citations: 0.

FERRAZ, RAUL ANTONIO;
FERREIRA, RUTH NASCIMENTO.
One-weight codes in some classes of group rings.
** APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING**,
NOV 2020.
Web of Science Citations: 0.

GIAMBRUNO, ANTONIO;
LA MATTINA, DANIELA;
MILIES, CESAR POLCINO.
STAR-FUNDAMENTAL ALGEBRAS: POLYNOMIAL IDENTITIES AND ASYMPTOTICS.
** TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY**,
v. 373,
n. 11,
p. 7869-7899,
NOV 2020.
Web of Science Citations: 1.

DOKUCHAEV, MIKHAILO;
KHRYPCHENKO, MYKOLA;
MAKUTA, MAYUMI.
The third partial cohomology group and existence of extensions of semilattices of groups by groups.
** FORUM MATHEMATICUM**,
v. 32,
n. 5,
p. 1297-1313,
SEP 2020.
Web of Science Citations: 0.

FERREIRA, VITOR O.;
GONCALVES, JAIRO Z.;
SANCHEZ, JAVIER.
Free Symmetric and Unitary Pairs in the Field of Fractions of Torsion-Free Nilpotent Group Algebras.
** ALGEBRAS AND REPRESENTATION THEORY**,
v. 23,
n. 3,
p. 605-619,
JUN 2020.
Web of Science Citations: 0.

SILVA, ANDERSON;
MILIES, C. POLCINO.
CYCLIC CODES OF LENGTH 2p(n) OVER FINITE CHAIN RINGS.
** Advances in Mathematics of Communications**,
v. 14,
n. 2,
p. 233-245,
MAY 2020.
Web of Science Citations: 0.

DOKUCHAEV, MIKHAILO;
KHRYPCHENKO, MYKOLA;
JACOBO SIMON, JUAN.
Globalization of group cohomology in the sense of Alvares-Alves-Redondo.
** Journal of Algebra**,
v. 546,
p. 604-640,
MAR 15 2020.
Web of Science Citations: 0.

GIAMBRUNO, ANTONIO;
MILIES, CESAR POLCINO;
ZAICEV, MIKHAIL.
A characterization of fundamental algebras through S-n-characters.
** Journal of Algebra**,
v. 541,
p. 51-60,
JAN 1 2020.
Web of Science Citations: 0.

SANCHEZ, JAVIER.
Free group algebras in division rings with valuation I.
** Journal of Algebra**,
v. 531,
p. 221-248,
AUG 1 2019.
Web of Science Citations: 0.

GONCALVES, JAIRO Z.
Free subgroups in k(x(1), ... , x(n))(X; sigma) and k(x, y)(X; sigma).
** FORUM MATHEMATICUM**,
v. 31,
n. 3,
p. 769-777,
MAY 2019.
Web of Science Citations: 0.

DOKUCHAEV, MIKHAILO;
KHRYPCHENKO, MYKOLA.
Partial cohomology of groups and extensions of semilattices of abelian groups.
** Journal of Pure and Applied Algebra**,
v. 222,
n. 10,
p. 2897-2930,
OCT 2018.
Web of Science Citations: 1.

SANCHEZ, JAVIER.
Obtaining free group algebras in division rings generated by group graded rings.
** JOURNAL OF ALGEBRA AND ITS APPLICATIONS**,
v. 17,
n. 10
OCT 2018.
Web of Science Citations: 1.

DOKUCHAEV, MIKHAILO;
KIRICHENKO, VLADIMIR;
KUDRYAVTSEVA, GANNA;
PLAKHOTNYK, MAKAR.
The max-plus algebra of exponent matrices of tiled orders.
** Journal of Algebra**,
v. 490,
p. 1-20,
NOV 15 2017.
Web of Science Citations: 0.

DOKUCHAEV, MIKHAILO;
KHRYPCHENKO, MYKOLA.
Twisted partial actions and extensions of semilattices of groups by groups.
** INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION**,
v. 27,
n. 7,
p. 887-933,
NOV 2017.
Web of Science Citations: 2.

GONCALVES, JAIRO Z.
Free pairs of symmetric and unitary units in normal subgroups of a division ring.
** JOURNAL OF ALGEBRA AND ITS APPLICATIONS**,
v. 16,
n. 6
JUN 2017.
Web of Science Citations: 1.

GONCALVES, JAIRO Z.
Free groups in a normal subgroup of the field of fractions of a skew polynomial ring.
** COMMUNICATIONS IN ALGEBRA**,
v. 45,
n. 12,
p. 5193-5201,
2017.
Web of Science Citations: 1.

Please report errors in scientific publications list by writing to:
cdi@fapesp.br.