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If for every elements $x$ and $y$ of an associative algebraic structure $(S,\cdot)$ there exists a positive integer $r$ such that $ab=b^ra$, then $S$ is called quasi-commutative. Evidently, every abelian group or commutative semigroup is quasi-commutative. Also every finite Hamiltonian group that may be considered as a semigroup, is quasi-commutative however, there are quasi-commutative semigroups which are non-group and non commutative. In this paper, we provide three finitely presented non-commutative semigroups which are quasi-commutative. These are the first given concrete examples of finite semigroups of this type.
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참고문헌 (11)
참고문헌 신청
A. C. Spoletini / 1980 / Quasicommutative semigroups and σ-reflexive semi-groups / Semigroup Forum 19 (4) : 313 ~ 321
A. C. Spoletini / 1983 / Quasi Hamiltonian semigroups / Czechoslovak Math. J 33 (1) : 131 ~ 140
A. H. Clifford / 1961 / The Algebraic Theory of Semigroups I / Amer. Math. Soc
B. Pondˇeliˇcek / 1985 / Note on Quasi-Hamiltonian semigroups / ˇCasopis pro pˇestov´an´ı matematiky 110 (4) : 356 ~ 358
C. M. Campbell / 1995 / Certain one-relator products of semigroups / Comm. Algebra 23 (14) : 5207 ~ 5219
A. C. Spoletini / 1983 / Quasi Hamiltonian semigroups / Czechoslovak Math. J 33 (1) : 131 ~ 140
A. H. Clifford / 1961 / The Algebraic Theory of Semigroups I / Amer. Math. Soc
B. Pondˇeliˇcek / 1985 / Note on Quasi-Hamiltonian semigroups / ˇCasopis pro pˇestov´an´ı matematiky 110 (4) : 356 ~ 358
C. M. Campbell / 1995 / Certain one-relator products of semigroups / Comm. Algebra 23 (14) : 5207 ~ 5219
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