##### Prof. Dr.rer.nat. Indah Emilia Wijayanti, M.Si.

*Head of Algebra Laboratory*

https://acadstaff.ugm.ac.id/indahewijayanti

Ind_Wijayanti@ugm.ac.id

Algebra is a branch of mathematics that studies mathematical symbols along with the rules for manipulating these symbols. Simple things in algebra such as finding solutions to equations are usually used in other disciplines, e.g. economics, engineering or applied mathematics. Meanwhile, abstractions that give rise to groups, rings and fields is an object of research for mathematicians.

Algebra is also the name of a system or mathematical structure. There are special algebras that become the object of research in the field of algebra, such as linear algebra, Lie algebra, (non)associative algebra, (non)commutative algebra, topological algebra etc. Furthermore, the approach through algebra is often added to the names of certain objects such as algebraic geometry, algebraic topology and algebraic graph.

Algebra Research Group has achievement to become a reference for theoretical algebra research in ring, module, number theory and graph, as well as collaborating with other fields to develop applied algebra. Including in the study of algebraic structures are semigroups, semirings, coalgebras, comodules and max-plus algebra.

The development of research in algebra is mostly motivated by observations on the properties of number theory. Moreover, the research of number theory involves a lot of combinatorial observations. These facts bring us to consider number theory, graph theory and combinatorics also as objects of our research.

We concern the topics around linear systems, coding theory and cryptography as the applications of algebra. In various mathematical modeling techniques, knowledge of matrices and their characteristics is needed. Therefore, we also conduct the knowledge of matrix analysis.

**Keywords:**

Dedekind and Krull modules

Unique factorization modules

Generalized NTRU (Ma-TRU, Matrix NTRU, GTRU, etc)

Generalized clean module (clean comodule, r-clean bimodule)

Generalized primeness of module (weakly (co)prime, weakly endo(co)prime module and comodule)

*-ring and *-module

Gröbner bases

Ring of differential operators

T[[S]]-Noetherian module

Generalized bases of modules

Graph labelling

Irregularity and h-irregularity strength

Graph operation

Graph over algebraic structures (connectivity, eulerianity, hamiltonicity, graph structure, independence number, domination number)

Partition theory

Algebraic number theory

Linear system over max-plus algebra