MA90142: Advanced Algebraic Structures

The module is designed to provide students with an advanced understanding of algebraic structures, with particular emphasis on non-associative algebras and their applications in geometry. It covers selected algebraic systems, including symmetric, dihedral, and quaternion groups, as well as quasigroups and loops, with further attention to the concepts of isotopy and parastrophy in quasigroups. The module also examines modules over a ring as a generalization of vector spaces in which scalars are drawn from a ring rather than a field. Topics in this area include left and right modules, submodules, module homomorphisms, quotient modules and isomorphism theorems, direct sums and products, injective and projective modules, free modules, finitely generated and Noetherian modules, exact sequences, module decomposition, and tensor products. In addition, the module considers pedagogical approaches for enhancing the teaching and learning of algebra across different levels of education.