NORMAL BCI/BCK-ALGEBRAS

  • Meng, Jie (Department of Mathematics Northwest University) ;
  • Wei, Shi-Ming (Institute of Mathematics Huaibei Coal Mining Teacher′s College) ;
  • Jun, Young-Bae (Department of Mathematics Education Gyeongsang National University)
  • 발행 : 1994.04.01

초록

In 1966, Iseki [2] introduced the notion of BCI-algebras which is a generalization of BCK-algebras. Lei and Xi [3] discussed a new class of BCI-algebra, which is called a p-semisimple BCI-algebra. For p-semisimple BCI-algebras, a subalgebra is an ideal. But a subalgebra of an arbitrary BCI/BCK-algebra is not necessarily an ideal. In this note, a BCI/BCK-algebra that every subalgebra is an ideal is called a normal BCI/BCK-algebra, and we give characterizations of normal BCI/BCK-algebras. Moreover we give a positive answer to the problem which is posed in [4].(omitted)

키워드