Algebraic interpretations of hyperbolic functions

Siriluk Donganont; Hee Sik Kim; Sun Shin Ahn; Choonkil Park

doi:10.2298/FIL2529339D

Algebraic interpretations of hyperbolic functions

Siriluk Donganont
, Hee Sik Kim
, Sun Shin Ahn
, Choonkil Park

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we obtain an algebraic interpretation of hyperbolic functions. By using four conditions, we define a hyperbolic algebra over reals, and we prove that linear groupoids or commutative cubic algebras cannot be a hyperbolic algebra, but the quadratic algebras can be hyperbolic algebras under some conditions.

Original language	English
Pages (from-to)	10339-10348
Number of pages	10
Journal	Filomat
Volume	39
Issue number	29
DOIs	https://doi.org/10.2298/FIL2529339D
State	Published - 2025

Keywords

(linear) groupoid
cubic algebra
hyperbolic
quadratic algebra

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title = "Algebraic interpretations of hyperbolic functions",

abstract = "In this paper, we obtain an algebraic interpretation of hyperbolic functions. By using four conditions, we define a hyperbolic algebra over reals, and we prove that linear groupoids or commutative cubic algebras cannot be a hyperbolic algebra, but the quadratic algebras can be hyperbolic algebras under some conditions.",

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author = "Siriluk Donganont and Kim, \{Hee Sik\} and Ahn, \{Sun Shin\} and Choonkil Park",

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AU - Ahn, Sun Shin

AU - Park, Choonkil

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AB - In this paper, we obtain an algebraic interpretation of hyperbolic functions. By using four conditions, we define a hyperbolic algebra over reals, and we prove that linear groupoids or commutative cubic algebras cannot be a hyperbolic algebra, but the quadratic algebras can be hyperbolic algebras under some conditions.

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KW - cubic algebra

KW - hyperbolic

KW - quadratic algebra

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DO - 10.2298/FIL2529339D

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Algebraic interpretations of hyperbolic functions

Abstract

Keywords

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