Alternative Loop Rings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Alternative Loop Rings write by E.G. Goodaire. This book was released on 1996-10-24. Alternative Loop Rings available in PDF, EPUB and Kindle. For the past ten years, alternative loop rings have intrigued mathematicians from a wide cross-section of modern algebra. As a consequence, the theory of alternative loop rings has grown tremendously. One of the main developments is the complete characterization of loops which have an alternative but not associative, loop ring. Furthermore, there is a very close relationship between the algebraic structures of loop rings and of group rings over 2-groups. Another major topic of research is the study of the unit loop of the integral loop ring. Here the interaction between loop rings and group rings is of immense interest. This is the first survey of the theory of alternative loop rings and related issues. Due to the strong interaction between loop rings and certain group rings, many results on group rings have been included, some of which are published for the first time. The authors often provide a new viewpoint and novel, elementary proofs in cases where results are already known. The authors assume only that the reader is familiar with basic ring-theoretic and group-theoretic concepts. They present a work which is very much self-contained. It is thus a valuable reference to the student as well as the research mathematician. An extensive bibliography of references which are either directly relevant to the text or which offer supplementary material of interest, are also included.
Alternative Loop Rings
Alternative Loop Rings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Alternative Loop Rings write by E.G. Goodaire. This book was released on 1996-11-07. Alternative Loop Rings available in PDF, EPUB and Kindle. For the past ten years, alternative loop rings have intrigued mathematicians from a wide cross-section of modern algebra. As a consequence, the theory of alternative loop rings has grown tremendously. One of the main developments is the complete characterization of loops which have an alternative but not associative, loop ring. Furthermore, there is a very close relationship between the algebraic structures of loop rings and of group rings over 2-groups. Another major topic of research is the study of the unit loop of the integral loop ring. Here the interaction between loop rings and group rings is of immense interest. This is the first survey of the theory of alternative loop rings and related issues. Due to the strong interaction between loop rings and certain group rings, many results on group rings have been included, some of which are published for the first time. The authors often provide a new viewpoint and novel, elementary proofs in cases where results are already known. The authors assume only that the reader is familiar with basic ring-theoretic and group-theoretic concepts. They present a work which is very much self-contained. It is thus a valuable reference to the student as well as the research mathematician. An extensive bibliography of references which are either directly relevant to the text or which offer supplementary material of interest, are also included.
Alternative Loop Rings with Solvable Unit Loops
Alternative Loop Rings with Solvable Unit Loops - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Alternative Loop Rings with Solvable Unit Loops write by Edgar G. Goodaire. This book was released on 1999. Alternative Loop Rings with Solvable Unit Loops available in PDF, EPUB and Kindle.
Symmetric Units in Alternative Loop Rings
Symmetric Units in Alternative Loop Rings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symmetric Units in Alternative Loop Rings write by Edgar G. Goodaire. This book was released on 2003. Symmetric Units in Alternative Loop Rings available in PDF, EPUB and Kindle.
Smarandache Non-Associative Rings
Smarandache Non-Associative Rings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Smarandache Non-Associative Rings write by W. B. Vasantha Kandasamy. This book was released on 2002. Smarandache Non-Associative Rings available in PDF, EPUB and Kindle. Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book. Thus, as a particular case: A Non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c in R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P in R, that is an associative ring (with respect to the same binary operations on R).
