论文标题
关于对称$ n $ - 亚军乐队的结构
On the structure of symmetric $n$-ary bands
论文作者
论文摘要
我们研究对称$ n $ ary乐队的类。这些是$ n $ -ary semigroups $（x，f）$，因此$ f $在排列和idempotent的行动下是不变的，即满足$ f（x，\ ldots，x）= x $ in x $中的所有$ x \ for x $。我们首先为这些对称的$ n $ ary频段提供了一个结构定理，该频段扩展了某些类别的频段的经典（强）半静力分解。我们介绍了$ n $ y-ary semigroups强的$ n $ y-ary半静脉曲张的概念，我们表明对称的$ n $ y-ary bands恰恰是$ n $ n $ n $ n $ n $ artertices of $ n $ n $ artertions的$ n $ y-arion-ary-ary-artions toberian tobers of Abelian集团的指数$ n-1 $ n-1 $。最后，我们使用结构定理来获得对称$ n $ ary频段的必要条件，以还原为半群。
We study the class of symmetric $n$-ary bands. These are $n$-ary semigroups $(X,F)$ such that $F$ is invariant under the action of permutations and idempotent, i.e., satisfies $F(x,\ldots,x)=x$ for all $x\in X$. We first provide a structure theorem for these symmetric $n$-ary bands that extends the classical (strong) semilattice decomposition of certain classes of bands. We introduce the concept of strong $n$-ary semilattice of $n$-ary semigroups and we show that the symmetric $n$-ary bands are exactly the strong $n$-ary semilattices of $n$-ary extensions of Abelian groups whose exponents divide $n-1$. Finally, we use the structure theorem to obtain necessary and sufficient conditions for a symmetric $n$-ary band to be reducible to a semigroup.
