Theory of Near-Rings

Robert Lockhart has worked in mathematics at universities in London, Nigeria, New Guinea, Brunei, Milton Keynes and Oxford, where he also worked simultaneously in computing. He has enjoyed a parallel career in computing, as one of the original programmer-designers for the multi award-winning British Telecom Prestel project, as part of a research project funded by the European Union, and at the Atlas laboratory for the Rutherford–Appleton laboratory. He has published research papers on algebra, conservation biology, and modern computing. For the past twenty years he has worked mainly in distance and online education. Throughout his career he has been a regular contributor to near-ring conferences and a member of the London Mathematical Society.

“This book is a substantial account … of almost all known aspects of near-ring theory. … It should therefore be regarded as a rich source of known results on various aspects of near-ring theory … . This makes the book an important asset to the near-ring researcher's library. … This book is a massive undertaking by the author, and he should be commended for it. … it is highly recommended to order the book for your library as an excellent work of reference.” (Johan H. Meyer, Mathematical Reviews, January, 2023)“The book is interesting, and could be useful to researchers and students.” (Bijan Davvaz, zbMATH 1498.16001, 2022)

• 1 Stems, Mappings and Near-Rings.- 2 Near-Ring Theory.- 3 Near-Fields.- 4 Near-Rings on Groups with Low Order.- 5 Near-Rings on Some Families of Groups.- 6 Near-Rings Hosted by p-Groups and Related Groups.- 7 Transformation Near-Rings.- 8 Generalisations and Sub-Near-Rings of Transformation Near-Rings.- 9 Phomomorphisms.- 10 Specific Examples.- 11 Modules.- 12 Radicals.- 13 Matrices.- 14 F-Near-Rings.- 15 Product Theory.- 16 Product Theory on Finite Elementary Abelian Groups.- A Isotopy.- B Near-Ring Products on D4.- C Other Structures of Interest.- D Semi-Linear Mappings.- E Zsigmondy's Theorem.- Bibliography.- Afterword.- Index.