On (*)-ideals and positive implicative ideals in bci-algebras

Hamza A. S. Abujabal, Jie Meng


In the present paper, we given sorne equivalent conditions of (*)-ideals and positive implicative ideals in BCI-algebras and we clarify the relation of the two classes of ideals. Also, we obtain further properties of these ideals. Finally, we discuss a quotient algebra of a BCI-algebra by a closed (*)-ideal and a quotient algebra by positive implicative ideal.

Palabras clave

BCI-algebra ; Closed ideal ; (*)-ideal ; Positive implicative ideal ; Quotient algebra

Texto completo:



S. A. Bhatti, Close-ness and open-ness of ideals in BCl-algebras, Math. Japan, 36, pp. 915-921, (1991).

C. S. Roo, Closed ideals and p-semisimple BCl-algebras, Math. Japon, 35, pp. 1103-1112, (1990).

C. S. Roo, Filters and ideals in BCl-algebras, Math. Japon, 36, pp. 987-997, (1991).

S. M. Hong, Y. B. Jun and J. Meng, On strong ideals and p-ideals in BCl-algebras, submitted.

K. Iséki, On ideals in BCK-algebras, Math. Seminar Notes, 3, pp. 1-12, (1975).

K. Iséki, On BCl-algebras, Math. Seminar Notes, 8, pp. 125-130, (1980).

T. D. Lei and C. C. Xi, p-radical in BCI-algebras, Math. Japon, 30, pp. 511-517, (1985).

J. Meng, On ideals in BCK-algebras, Math. Japon, 40, pp. 143-154, (1994).

J. Meng and H. A. S. Abujabal, On closed ideals in BCI-algebras, submitted.

J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon SaCo., Seoul, Korea, (1994).

J. Meng and S. M. Wei, Periodic BCI-algebras and closed ideals in BCI-algebras, Math. Japon, 38, pp. 571-575, (1993).

J. Meng and X. L. Xin, Characterizations of atoms in BCI-algebras, Math. Japon, 37, pp. 359-361, (1992).

E. H. Roh, Y. B. Jun and S. M. Wei, Some ideals in BCI-algebras, Math. Japon, to appear.

C. C. Xi, On a class of BCI-algebras, Math. Japon, 35, pp. 13-17, (1990).

Q. Zhang, BCI-algebras with weak units, Math. Japon, 36, pp. 1163-1166, (1991).

X. H. Zhang, On p-ideals of a BCI-algebras, Math. Japon, submitted.

DOI: http://dx.doi.org/10.22199/S07160917.1999.0002.00007

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