论文标题
无限等级的无扭转组的乘法组
Multiplication Groups of Abelian Torsion-Free Groups of Finite Rank
论文作者
论文摘要
对于Abelian $ g $，任何同构$μ\ colon g \ otimes g \ rightarrow g $在$ g $上称为a \ textsf {乘法}。 Abelian Group $ g $上所有乘法的集合$ \ text {Mult} \，G $本身是Abelian组相对于添加的组；该组称为$ g $的\ textsf {乘法组}。令$ \ MATHCAL {A} _0 $为所有减少的块固定的类，几乎完全可分解的戒指类型组，带有环状调节器商。在本文中，对于$ g \ in \ mathcal {a} _0 $，我们描述了$ \ text {mult} \，g $。我们证明，对于$ g \ in \ Mathcal {a} _0 $，组$ \ text {mult} \，g $也属于类$ \ mathcal {a} _0 $。对于\ Mathcal {a} _0 $中的任何组$ g \，我们描述了等级，调节器，调节器索引，近同构的不变性，主要分解以及组的标准表示$ \ text {mult} {mult} \，g $。
For an Abelian group $G$, any homomorphism $μ\colon G\otimes G\rightarrow G$ is called a \textsf{multiplication} on $G$. The set $\text{Mult}\,G$ of all multiplications on an Abelian group $G$ itself is an Abelian group with respect to addition; the group is called the \textsf{multiplication group} of $G$. Let $\mathcal{A}_0$ be the class of all reduced block-rigid almost completely decomposable groups of ring type with cyclic regulator quotient. In this paper, for groups $G\in \mathcal{A}_0$, we describe groups $\text{Mult}\,G$. We prove that for $G\in \mathcal{A}_0$, the group $\text{Mult}\,G$ also belongs to the class $\mathcal{A}_0$. For any group $G\in \mathcal{A}_0$, we describe the rank, the regulator, the regulator index, invariants of near-isomorphism, a main decomposition, and a standard representation of the group $\text{Mult}\,G$.
