π½-valued trace of a finite-dimensional commutative π½-algebra
A non-zero π½-valued π½-linear map on a finite dimensional π½-algebra is called an π½-valued trace if its kernel does not contain any non-zero ideals. However, given an π½-algebra such a map may not always exist. We find an infinite class of finite-dimensional commutative π½-algebras which admit an π½-valued trace. In fact, in these cases, we explicitly construct a trace map. The existence of an π½-valued trace on a finite dimensional commutative π½-algebra induces a non-degenerate bilinear form on the π½-algebra which may be helpful both theoretically and computationally. In this article, we suggest a couple of applications of an π½-valued trace map of an π½-algebra to algebraic coding theory.
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