Difference between revisions of "BCH-algebra"
From Encyclopedia of Mathematics
(LaTeX) |
(→References: expand bibliodata) |
||
Line 11: | Line 11: | ||
====References==== | ====References==== | ||
<table> | <table> | ||
− | <TR><TD valign="top">[a1]</TD> <TD valign="top"> Qing-ping Hu, Xin Li, "On BCH-algebras" ''Math. Seminar Notes (Kobe University)'' , '''11''' (1983) pp. 313–320</TD></TR> | + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> Qing-ping Hu, Xin Li, "On BCH-algebras" ''Math. Seminar Notes (Kobe University)'' , '''11''' (1983) pp. 313–320 {{ZBL|0579.03047}}</TD></TR> |
− | <TR><TD valign="top">[a2]</TD> <TD valign="top"> Y. Imai, K. Iséki, "On axiom systems of propositional calculi, XIV" ''Proc. Japan Acad. Ser. A Math. Sci.'' , '''42''' (1966) pp. 19–22</TD></TR> | + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> Y. Imai, K. Iséki, "On axiom systems of propositional calculi, XIV" ''Proc. Japan Acad. Ser. A Math. Sci.'' , '''42''' (1966) pp. 19–22 {{DOI|10.3792/pja/1195522169}} {{MR|0195704}} {{ZBL|0156.24812}}</TD></TR> |
− | <TR><TD valign="top">[a3]</TD> <TD valign="top"> K. Iséki, "An algebra related with a propositional calculus" ''Proc. Japan Acad. Ser. A, Math. Sci.'' , '''42''' (1966) pp. 26–29</TD></TR> | + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> K. Iséki, "An algebra related with a propositional calculus" ''Proc. Japan Acad. Ser. A, Math. Sci.'' , '''42''' (1966) pp. 26–29 {{DOI|10.3792/pja/1195522171}} {{MR|0202571}} {{ZBL|0207.29304}}</TD></TR> |
</table> | </table> |
Revision as of 21:29, 12 December 2014
A variant of a BCI-algebra. One can define it by taking some of the axioms for a BCI-algebra and some of the important properties of a BCI-algebra. Specifically, a BCH-algebra is a non-empty set $X$ with a constant $0$ and a binary relation $*$ satisfying the following axioms:
1) $x * x = 0$;
2) if $x * y = 0$ and $y * x = 0$, then $x = y$;
3) $(x*y)*z = (x*z)*y$. Clearly a BCI-algebra is a BCH-algebra; however, the converse is not true. While some work has been done on such algebras, generally they have not been as extensively investigated as BCI-algebras.
References
[a1] | Qing-ping Hu, Xin Li, "On BCH-algebras" Math. Seminar Notes (Kobe University) , 11 (1983) pp. 313–320 Zbl 0579.03047 |
[a2] | Y. Imai, K. Iséki, "On axiom systems of propositional calculi, XIV" Proc. Japan Acad. Ser. A Math. Sci. , 42 (1966) pp. 19–22 DOI 10.3792/pja/1195522169 MR0195704 Zbl 0156.24812 |
[a3] | K. Iséki, "An algebra related with a propositional calculus" Proc. Japan Acad. Ser. A, Math. Sci. , 42 (1966) pp. 26–29 DOI 10.3792/pja/1195522171 MR0202571 Zbl 0207.29304 |
How to Cite This Entry:
BCH-algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=BCH-algebra&oldid=35595
BCH-algebra. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=BCH-algebra&oldid=35595
This article was adapted from an original article by C.S. Hoo (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article