http://hdl.handle.net/11320/20996 2026-09-14T21:12:27Z http://hdl.handle.net/11320/21012 Tytuł: Convex Sets and Convex Combinations on Complex Linear Spaces Autorzy: Matsuzaki, Hidenori; Endou, Noboru; Shidama, Yasunari Abstrakt: In this article, convex sets, convex combinations and convex hulls on complex linear spaces are introduced. 2008-01-01T00:00:00Z http://hdl.handle.net/11320/21011 Tytuł: Banach Algebra of Bounded Functionals Autorzy: Shidama, Yasunari; Suzuki, Hikofumi; Endou, Noboru Abstrakt: Inthisarticle, we describe some basic properties of the Banach algebra which is constructed from all bounded functionals. 2008-01-01T00:00:00Z http://hdl.handle.net/11320/21010 Tytuł: Ideals of BCI-algebras and their Properties Autorzy: Wu, Chenglong; Ding, Yuzhong Abstrakt: In this article three classes of ideals are discussed: associative ideals, commutative ideals, implicative ideals and positive implicative ideals, and their elementary properties. Some of their properties and the relationships between them have not been proven yet, and will be completed in the following article. 2008-01-01T00:00:00Z http://hdl.handle.net/11320/21008 Tytuł: Uniqueness of Factoring an Integer and Multiplicative Group Z/pZ Autorzy: Okazaki, Hiroyuki; Shidama, Yasunari Abstrakt: In the [20], it had been proven that the Integers modulo p, in this article we shall refer as Z/pZ, constitutes a field if and only if p is a prime. Then the prime modulo Z/pZ is an additive cyclic group and Z/pZ∗ = Z/pZ\{0} is a multiplicative cyclic group, too. The former has been proven in the [23]. However, the latter had not been proven yet. In this article, first, we prove a theorem concerning the LCM to prove the existence of primitive elements of Z/p∗. Moreover we prove the uniqueness of factoring an integer. Next we define the multiplicative group Z/pZ∗ and prove it is cyclic. 2008-01-01T00:00:00Z