Smarandache Semirings, Semifields and Semivector Spaces
by W. B. Vasantha Kandasamy
Publisher: American Research Press 2002
Number of pages: 122
This is the first book on the Smarandache algebraic structures that have two binary operations. Semirings are algebraic structures with two binary operations enjoying several properties and it is the most generalized structure -- for all rings and fields are semirings.
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by Michael Artin
From the table of contents: Morita equivalence (Hom, Bimodules, Projective modules ...); Localization and Goldie's theorem; Central simple algebras and the Brauer group; Maximal orders; Irreducible representations; Growth of algebras.
by G.H.E. Duchamp, et al. - arXiv
This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics.
by W. B. Vasantha Kandasamy - American Research Press
The purpose of this book entirely lies in the study, introduction and examination of the Smarandache loops. We expect the reader to have a good background in algebra and more specifically a strong foundation in loops and number theory.
by Shlomo Sternberg
The Campbell Baker Hausdorff formula, sl(2) and its representations, classical simple algebras, Engel-Lie-Cartan-Weyl, conjugacy of Cartan subalgebras, simple finite dimensional algebras, cyclic highest weight modules, Serre’s theorem, and more.