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On Topological Bihyperbolic Modules
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In this paper, we introduce topological modules over the ring of bihyperbolic numbers. We discuss bihyperbolic convexity, bihyperbolic-valued seminorms and bihyperbolic-valued Minkowski functionals in topological bihyperbolic modules. Finally we introduce locally bihyperbolic convex modules.
Keywords
Bihyperbolic Modules, Topological Bihyperbolic Modules, Bihyperbolic Convexity, Bihyperbolic-Valued Seminorms, Bihyperbolic-Valued Minkowski Functionals, Locally Bihyperbolic Convex Modules.
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- M. Bilgin and S. Ersoy, Algebraic properties of bihyperbolic numbers, Advances in Applied Clifford Algebras, 30 (1):13(2020).
- J. Cockle, On certain functions resembling quaternions and on a new imaginary in algebra, Lond-Dublin-Edinb. Philos. Mag., 3 (33)(1848), 435-439.
- R. Kumar, R. Kumar and D. Rochon, The fundamental theorems in the framework of bicomplex topological modules, arXiv: 1109.3424v1(2011).
- R. Kumar and H. Saini, Topological bicomplex modules, Adv. Appl. Clifford Algebras, 26 (4)(2016), 1249-1270.
- R. Larsen, Functional Analysis: An Introduction, Marcel Dekker, New York 1973.
- M. E. Luna-Elizarraras, C. O. Perez-Regalado and M. Shapiro, On linear functionals and Hahn–Banach theorems for hyperbolic and bicomplex modules, Adv. Appl. Clifford Algebras, 24 (2014), 1105-1129.
- L. Narici and E. Beckenstein, Topological Vector Spaces, Marcel Dekker, New York 1985.
- S. Olariu, Complex Numbers in n-dimensions, North-Holland Mathematics Studies, Elsevier, Amsterdam, Boston, 190 (2002), 51-148.
- A. A. Pogorui, R. M. Rodriguez-Dagnino and R. D. Rodrigue-Said, On the set of zeros of bihyperbolic polynomials, Complex Var. Elliptic Equ. 53 (7)(2008), 685-690.
- W. Rudin, Functional Analysis, 2nd edn., McGraw Hill, New York 1991.
- C. Segre, Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici (The real representation of complex elements and hyperalgebraic entities), Math. Ann., 40 (1892), 413-467.
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