Subtraction algebras and B C K -algebras

Young Hee Kim; Hee Sik Kim

Mathematica Bohemica (2003)

  • Volume: 128, Issue: 1, page 21-24
  • ISSN: 0862-7959

Abstract

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In this note we show that a subtraction algebra is equivalent to an implicative B C K -algebra, and a subtraction semigroup is a special case of a B C I -semigroup.

How to cite

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Kim, Young Hee, and Kim, Hee Sik. "Subtraction algebras and $BCK$-algebras." Mathematica Bohemica 128.1 (2003): 21-24. <http://eudml.org/doc/249225>.

@article{Kim2003,
abstract = {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.},
author = {Kim, Young Hee, Kim, Hee Sik},
journal = {Mathematica Bohemica},
keywords = {subtraction algebra; subtraction semigroup; implicative $BCK$-algebra; $BCI$-semigroup; subtraction algebra; subtraction semigroup; implicative BCK-algebra; BCI-semigroup},
language = {eng},
number = {1},
pages = {21-24},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Subtraction algebras and $BCK$-algebras},
url = {http://eudml.org/doc/249225},
volume = {128},
year = {2003},
}

TY - JOUR
AU - Kim, Young Hee
AU - Kim, Hee Sik
TI - Subtraction algebras and $BCK$-algebras
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 1
SP - 21
EP - 24
AB - 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.
LA - eng
KW - subtraction algebra; subtraction semigroup; implicative $BCK$-algebra; $BCI$-semigroup; subtraction algebra; subtraction semigroup; implicative BCK-algebra; BCI-semigroup
UR - http://eudml.org/doc/249225
ER -

References

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  4. Fuzzy I -ideals in B C I -semigroups, Southeast Asian Bull. Math. 22 (1998), 147–153. (1998) MR1684225
  5. B C I -semigroups, Honam Mathematical J. 15 (1993), 59–64. (1993) MR1238590
  6. Fuzzy commutative I -ideals in B C I -semigroups, J. Fuzzy Math. 5 (1997), 889–898. (1997) MR1488035
  7. B C K -algebras, Kyung Moon Sa Co., Seoul, 1994. (1994) MR1297121
  8. a & I -ideals on I S -algebras, Sci. Math. Japonicae Online 4 (2001), 21–25. (2001) MR1821605
  9. 10.1080/00927879208824453, Commun. Algebra 20 (1992), 2153–2169. (1992) Zbl0798.20058MR1172654DOI10.1080/00927879208824453
  10. On a system of axioms of a commutative B C K -algebras, Math. Seminar Notes 5 (1977), 255–256. (1977) MR0457314
  11. Subtraction semigroups, Math. Bohem. 120 (1995), 445–447. (1995) Zbl0851.20057MR1415091

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