Reality-Based Algebras,Generalized Camina-Frobenius Pairs,and the Nonexistence of Degree Maps |
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| Authors: | Harvey I. Blau Gang Chen |
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| Affiliation: | 1. Department of Mathematical Sciences , Northern Illinois University , DeKalb , Illinois , USA blau@math.niu.edu;3. School of Mathematics and Statistics , Central China Normal University , Wuhan , China |
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| Abstract: | The notion of a generalized Camina-Frobenius pair is extended to reality-based algebras, and a construction that characterizes such pairs is given. Zero-product sets are defined, and a best-possible upper bound on their size is proved and related to Camina-Frobenius pairs. It is shown that there exist commutative reality-based algebras with zero-product sets and, hence, no degree map, of every dimension at least 4. All such 4-dimensional algebras are constructed explicitly. |
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| Keywords: | Camina-Frobenius pair Degree map Fusion ring Hoheisel algebra Linear character Reality-based algebra Table algebra |
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