| Title:
|
Subtraction algebras and $BCK$-algebras (English) |
| Author:
|
Kim, Young Hee |
| Author:
|
Kim, Hee Sik |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
1 |
| Year:
|
2003 |
| Pages:
|
21-24 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we show that a subtraction algebra is equivalent to an implicative $BCK$-algebra, and a subtraction semigroup is a special case of a $BCI$-semigroup. (English) |
| Keyword:
|
subtraction algebra |
| Keyword:
|
subtraction semigroup |
| Keyword:
|
implicative $BCK$-algebra |
| Keyword:
|
$BCI$-semigroup |
| MSC:
|
06F35 |
| idZBL:
|
Zbl 1014.06018 |
| idMR:
|
MR1973421 |
| DOI:
|
10.21136/MB.2003.133931 |
| . |
| Date available:
|
2009-09-24T22:06:26Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133931 |
| . |
| Reference:
|
[1] J. C. Abbott: Semi-Boolean Algebras.Matemat. Vesnik 4 (1967), 177–198. MR 0239957 |
| Reference:
|
[2] J. C. Abbott: Sets, Lattices and Boolean Algebras.Allyn and Bacon, Boston, 1969. Zbl 0222.06001, MR 0242723 |
| Reference:
|
[3] S. S. Ahn, H. S. Kim: A note on $I$-ideals in $BCI$-semigroups.Comm. Korean Math. Soc. 11 (1996), 895–902. MR 1434849 |
| Reference:
|
[4] Y. B. Jun, S. S. Ahn, J. Y. Kim, H. S. Kim: Fuzzy $I$-ideals in $BCI$-semigroups.Southeast Asian Bull. Math. 22 (1998), 147–153. MR 1684225 |
| Reference:
|
[5] Y. B. Jun, S. M. Hong, E. H. Roh: $BCI$-semigroups.Honam Mathematical J. 15 (1993), 59–64. MR 1238590 |
| Reference:
|
[6] Y. B. Jun, J. Y. Kim, Y. H. Kim, H. S. Kim: Fuzzy commutative $I$-ideals in $BCI$-semigroups.J. Fuzzy Math. 5 (1997), 889–898. MR 1488035 |
| Reference:
|
[7] J. Meng, Y. B. Jun: $BCK$-algebras.Kyung Moon Sa Co., Seoul, 1994. MR 1297121 |
| Reference:
|
[8] E. H. Roh, S. Y. Kim, W. H. Shim: $a \& I$-ideals on $IS$-algebras.Sci. Math. Japonicae Online 4 (2001), 21–25. MR 1821605 |
| Reference:
|
[9] B. M. Schein: Difference semigroups.Commun. Algebra 20 (1992), 2153–2169. Zbl 0798.20058, MR 1172654, 10.1080/00927879208824453 |
| Reference:
|
[10] H. Yutani: On a system of axioms of a commutative $BCK$-algebras.Math. Seminar Notes 5 (1977), 255–256. MR 0457314 |
| Reference:
|
[11] B. Zelinka: Subtraction semigroups.Math. Bohem. 120 (1995), 445–447. Zbl 0851.20057, MR 1415091 |
| . |
