An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Homogeneous Integral Table Algebras of Degree Three: A Trilogy

Harvey I. Blau Northern Illinois University, DeKalb, IL
Bangteng Xu Northern Illinois University, DeKalb, IL
Z. Arad Bar-Ilan University, Ramat-Gan, Israel
E. Fisman Bar-Ilan University, Ramat-Gan, Israel
V. Miloslavsky Bar-Ilan University, Ramat-Gan, Israel
M. Muzychuk Bar-Ilan University, Ramat-Gan, Israel
Available Formats:
Electronic ISBN: 978-1-4704-0275-4
Product Code: MEMO/144/684.E
List Price: $51.00 MAA Member Price:$45.90
AMS Member Price: $30.60 Click above image for expanded view Homogeneous Integral Table Algebras of Degree Three: A Trilogy Harvey I. Blau Northern Illinois University, DeKalb, IL Bangteng Xu Northern Illinois University, DeKalb, IL Z. Arad Bar-Ilan University, Ramat-Gan, Israel E. Fisman Bar-Ilan University, Ramat-Gan, Israel V. Miloslavsky Bar-Ilan University, Ramat-Gan, Israel M. Muzychuk Bar-Ilan University, Ramat-Gan, Israel Available Formats:  Electronic ISBN: 978-1-4704-0275-4 Product Code: MEMO/144/684.E  List Price:$51.00 MAA Member Price: $45.90 AMS Member Price:$30.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1442000; 89 pp
MSC: Primary 13; 20; 05; 16;

Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three.

On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism of order three.

Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.

Graduate students and research mathematicians interested in commutative rings and algebras.

• Chapters
• I. Homogeneous integral table algebras of degree three with a faithful real element
• II. On antisymmetric homogeneous integral table algebras of degree three
• III. Homogeneous integral table algebras of degree three with no nontrivial linear elements
• Request Review Copy
• Get Permissions
Volume: 1442000; 89 pp
MSC: Primary 13; 20; 05; 16;

Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three.

On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism of order three.

Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.