Alternative Loop Rings, Volume 184 (north-holland Mathematics Studies)
by E.G. Goodaire /
1996 / English / PDF
14.2 MB Download
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.
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.
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.
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.
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.
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.