On (*)-ideals and positive implicative ideals in bci-algebras
DOI:
https://doi.org/10.22199/S07160917.1999.0002.00007Keywords:
BCI-algebra, Closed ideal, (*)-ideal, Positive implicative ideal, Quotient algebraAbstract
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.
References
1. S. A. Bhatti, Close-ness and open-ness of ideals in BCl-algebras, Math. Japan, 36, pp. 915-921, (1991).
2. C. S. Roo, Closed ideals and p-semisimple BCl-algebras, Math. Japon, 35, pp. 1103-1112, (1990).
3. C. S. Roo, Filters and ideals in BCl-algebras, Math. Japon, 36, pp. 987-997, (1991).
4. S. M. Hong, Y. B. Jun and J. Meng, On strong ideals and p-ideals in BCl-algebras, submitted.
5. K. Iséki, On ideals in BCK-algebras, Math. Seminar Notes, 3, pp. 1-12, (1975).
6. K. Iséki, On BCl-algebras, Math. Seminar Notes, 8, pp. 125-130, (1980).
7. T. D. Lei and C. C. Xi, p-radical in BCI-algebras, Math. Japon, 30, pp. 511-517, (1985).
8. J. Meng, On ideals in BCK-algebras, Math. Japon, 40, pp. 143-154, (1994).
9. J. Meng and H. A. S. Abujabal, On closed ideals in BCI-algebras, submitted.
10. J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon SaCo., Seoul, Korea, (1994).
11. J. Meng and S. M. Wei, Periodic BCI-algebras and closed ideals in BCI-algebras, Math. Japon, 38, pp. 571-575, (1993).
12. J. Meng and X. L. Xin, Characterizations of atoms in BCI-algebras, Math. Japon, 37, pp. 359-361, (1992).
13. E. H. Roh, Y. B. Jun and S. M. Wei, Some ideals in BCI-algebras, Math. Japon, to appear.
14. C. C. Xi, On a class of BCI-algebras, Math. Japon, 35, pp. 13-17, (1990).
15. Q. Zhang, BCI-algebras with weak units, Math. Japon, 36, pp. 1163-1166, (1991).
16. X. H. Zhang, On p-ideals of a BCI-algebras, Math. Japon, submitted.
2. C. S. Roo, Closed ideals and p-semisimple BCl-algebras, Math. Japon, 35, pp. 1103-1112, (1990).
3. C. S. Roo, Filters and ideals in BCl-algebras, Math. Japon, 36, pp. 987-997, (1991).
4. S. M. Hong, Y. B. Jun and J. Meng, On strong ideals and p-ideals in BCl-algebras, submitted.
5. K. Iséki, On ideals in BCK-algebras, Math. Seminar Notes, 3, pp. 1-12, (1975).
6. K. Iséki, On BCl-algebras, Math. Seminar Notes, 8, pp. 125-130, (1980).
7. T. D. Lei and C. C. Xi, p-radical in BCI-algebras, Math. Japon, 30, pp. 511-517, (1985).
8. J. Meng, On ideals in BCK-algebras, Math. Japon, 40, pp. 143-154, (1994).
9. J. Meng and H. A. S. Abujabal, On closed ideals in BCI-algebras, submitted.
10. J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon SaCo., Seoul, Korea, (1994).
11. J. Meng and S. M. Wei, Periodic BCI-algebras and closed ideals in BCI-algebras, Math. Japon, 38, pp. 571-575, (1993).
12. J. Meng and X. L. Xin, Characterizations of atoms in BCI-algebras, Math. Japon, 37, pp. 359-361, (1992).
13. E. H. Roh, Y. B. Jun and S. M. Wei, Some ideals in BCI-algebras, Math. Japon, to appear.
14. C. C. Xi, On a class of BCI-algebras, Math. Japon, 35, pp. 13-17, (1990).
15. Q. Zhang, BCI-algebras with weak units, Math. Japon, 36, pp. 1163-1166, (1991).
16. X. H. Zhang, On p-ideals of a BCI-algebras, Math. Japon, submitted.
Published
2018-04-04
How to Cite
[1]
H. A. S. Abujabal and J. Meng, “On (*)-ideals and positive implicative ideals in bci-algebras”, Proyecciones (Antofagasta, On line), vol. 18, no. 2, pp. 195-205, Apr. 2018.
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