Exponential Algebra: As an Extension of Topological Algebra - Halder, Prithwiraj
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In this book, we have introduced the concept of `\textit{exponential algebra}' (in short \textit{ealg}) by defining an internal multiplication on an evs over some field $ K $. We have explained that the concept of exponential algebra can be thought of as a generalisation of `algebra' in the sense that every exponential algebra contains an algebra; conversely, any algebra can be embedded into an exponential algebra. We develop a quotient structure on an ealg $X$ over some field $K$ by using the concept of congruence and topologise it. We introduce the concept of \emph{ideal}, \emph{semiideal}…mehr

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Produktbeschreibung
In this book, we have introduced the concept of `\textit{exponential algebra}' (in short \textit{ealg}) by defining an internal multiplication on an evs over some field $ K $. We have explained that the concept of exponential algebra can be thought of as a generalisation of `algebra' in the sense that every exponential algebra contains an algebra; conversely, any algebra can be embedded into an exponential algebra. We develop a quotient structure on an ealg $X$ over some field $K$ by using the concept of congruence and topologise it. We introduce the concept of \emph{ideal}, \emph{semiideal} and \emph{maximal ideal} of an ealg. We have shown that the hyperspace $\com{\X}{}$ (the set of all nonempty compact subsets of a Hausdorff topological algebra $\X$) is a topological exponential algebra over the field $\K$ of real or complex. We explore the function spaces in light of exponential algebra. It has been shown that the space of positive measures $\mathscr M(G)$ on a locally compact Housdorff topological group $G$, which are finite on each compact subset of $G$ is a topological ealg. Finally, we found a topological ealg with the help of Hausdorff metric.
Autorenporträt
Prithwiraj Halder completed his Ph.D. from University of Calcutta, India. His research area are Functional Analysis, Real Analysis, Operator Theory. His research article has been published in many international Journal. He is an Assistant Professor of Department of Mathematics, Bangabasi Morning College, Kolkata.