论文标题
Grothendieck组的多核类似物
Polyadic analog of Grothendieck group
论文作者
论文摘要
我们将MONOID（是代数$ k $ - 理论的起点）的完整组的Grothendieck构建概括为多层案例，而初始的Semigroup为$ M $ - $ - $ M $ - AR，而相应的最终类$ k_ {0} $可以是$ n $ y-ary。与二进制案例相反：1）可以有不同的多核直接产品，可以从一个多层半群中构建； 2）课程组的最终arity $ n $可能与初始半群的Arity $ m $不同； 3）交换性初始$ m $ - yar-ary semigroups可能导致非交通级$ n $ - y-ary组； 4）最初的$ M $ -ARY SEMIGROUP不需要该标识才能获得$ n $ ary组的类别，而这又可能完全没有身份。提出的数值示例表明，多核完成组的性质比二进制案例相比具有相当复杂的结构。
We generalize the Grothendieck construction of the completion group for a monoid (being the starting point of the algebraic $K$-theory) to the polyadic case, when an initial semigroup is $m$-ary and the corresponding final class group $K_{0}$ can be $n$-ary. As opposed to the binary case: 1) there can be different polyadic direct products which can be built from one polyadic semigroup; 2) the final arity $n$ of the class groups can be different from the arity $m$ of initial semigroup; 3) commutative initial $m$-ary semigroups can lead to noncommutative class $n$-ary groups; 4) the identity is not necessary for initial $m$-ary semigroup to obtain the class $n$-ary group, which in its turn can contain no identity at all. The presented numerical examples show that the properties of the polyadic completion groups are considerably nontrivial and have more complicated structure than in the binary case.
