Finite left distributive algebras with one generator
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- 作者：Drá ; pal ; Ale&scaron
- 关键词：Primary 20N02 ; secondary 08A05
- 刊名：Journal of Pure and Applied Algebra
- 出版年：1997
- 出版时间：October 10, 1997
- 年：1997
- 卷：121
- 期：3
- 页码：233-251
- 全文大小：946 K
文摘
Finite monogenerated groupoids G satisfying the left distributive law x · (y · z) = (x · y) · (x · z) are studied. They are shown to reduce over qG = {(a, b) 
G2; ca = cb for all c G} and pG = {(a, b) G2; ac = bc for all c G} to a groupoid isomorphic to Ak = Ak(*), k ≥ 0. (Ak is the unique left distributive groupoid on {1,…,2k} with a * 1 ≡ a + 1 mod 2k for every 1 ≤ a ≤ 2k.) G 
Ak is proved to hold whenever b 
a · b equals idG for some a G. We describe all cases when G = Ga 
{b} for some a, b G, and all cases when there exists a binary operation 
on G such that G(·, ) satisfies the axioms of left distributive algebras.
G2; ca = cb for all c G} and pG = {(a, b) G2; ac = bc for all c G} to a groupoid isomorphic to Ak = Ak(*), k ≥ 0. (Ak is the unique left distributive groupoid on {1,…,2k} with a * 1 ≡ a + 1 mod 2k for every 1 ≤ a ≤ 2k.) G Ak is proved to hold whenever b a · b equals idG for some a G. We describe all cases when G = Ga {b} for some a, b G, and all cases when there exists a binary operation on G such that G(·, ) satisfies the axioms of left distributive algebras.