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On left derivations of $BCH$-algebras

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In this paper, we introduce the notion of left derivations of $BCH$ algebras and investigate some properties of left derivations in a $BCH$-algebra. Moreover, we introduce the notions of fixed set and kernel set of derivations in a $BCH$-algebra and obtained some interesting properties in medial $BCH$-algebras. Also, we discuss the relations between ideals in a medial $BCH$-algebras.

Abstract

In this paper, we introduce the notion of left derivations of $BCH$ algebras and investigate some properties of left derivations in a $BCH$-algebra. Moreover, we introduce the notions of fixed set and kernel set of derivations in a $BCH$-algebra and obtained some interesting properties in medial $BCH$-algebras. Also, we discuss the relations between ideals in a medial $BCH$-algebras.

참고문헌 (6)

  1. M. A. Chaudhry, "On BCH-algebras", Math. Japonica, 36(4), pp.665~676 (1991)
  2. M. A. Chaudhry, "Ideals and Filter in BCH-algebras", Math. Japonica, 44(1), pp.101~112 (1996)
  3. Q. P. Hu, "On BCH-algebra", Math. Sem. Notes Kobe Univ, 11(2), pp.313~320 (1983)
  4. Q. P. Hu, "On proper BCH-algebra", Math. Japon, 30(4), pp.659~661 (1985)
  5. K. Iseki, "An algebra related with a propositional calculus", Proc. Japon Acad, 42, pp.26~29 (1966)
  6. Y. Imai, "On axiom system of propositional calculi XIV", Proc. Japan ACademy, 42, pp.19~22 (1966)

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