BRACKET FUNCTIONS ON GROUPOIDS

被引：1

作者：

Allen, Paul J. ^{[1
]}

Kim, Hee Sik ^{[2
]}

Neggers, Joseph ^{[1
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

[2] Hanyang Univ, Dept Math, Res Inst Nat Sci, Seoul 04763, South Korea

来源：

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY | 2019年 / 34卷 / 02期

关键词：

bracket function; e-bracket image algebra; e-bracket-abelian; d/B/BCK-algebra; Smarandache disjoint; Bin(X);

D O I：

10.4134/CKMS.c180136

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce an operation denoted by [Br-e], a bracket operation, which maps an arbitrary groupoid (X, *) on a set X to another groupoid (X, .) = [Br-e](X, *) which on groups corresponds to sending a pair of elements (x, y) of X to its commutator xyx(-l) y(-1). When applied to classes such as d-algebras, BCK-algebras, a variety of results is obtained indicating that this construction is more generally useful than merely for groups where it is of fundamental importance.

引用

页码：375 / 381

页数：7

共 16 条

[1]

Allen P. J., 2005, SCI MATH JPN, V61, P447

[2] LOCALLY-ZERO GROUPOIDS AND THE CENTER OF BIN (X) [J].

Fayoumi, Hiba F. .

COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2011, 26 (02) :163-168

[3]

Iorgulescu A., 2008, Algebras of Logic as BCK Algebras

[4]

Is6ki K., 1978, Math, V23, P1

[5]

Iseki K, 1980, MATH SEMINAR NOTES, V8, P125

[6]

JUN Y. B., 2000, J FUZZY MATH, V8, P123

[7] ANOTHER AXIOMATIZATION OF B-ALGEBRAS [J].

Kim, Chang Bum ;

Kim, Hee Sik .

DEMONSTRATIO MATHEMATICA, 2008, 41 (02) :259-262

[8] THE SEMIGROUPS OF BINARY SYSTEMS AND SOME PERSPECTIVES [J].

Kim, Hee Sik ;

Neggers, Joseph .

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2008, 45 (04) :651-661

[9]

Lee YC, 1999, MATH SLOVACA, V49, P27

[10]

Meng J., 1994, BCK-Algebras

← 1 2 →