发表机构
University of Zagreb（萨格勒布大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究确定了上三角整数矩阵环中Jordan D(N)-集存在无限集的N的条件，明确了有限集的最大基数，还给出了两类特殊无限集存在的充要条件。
AI 中文摘要
设U为2×2上三角整数矩阵构成的环。对N∈U，Jordan D(N)-集是U中不同非零矩阵构成的集合，满足对任意两个不同元素A、B，(AB+BA)/2 + N是U中的平方元。我们确定了所有使得无限Jordan D(N)-集存在的N；若不存在无限集，则每个此类集合至多有6个元素；若N不是U中两个平方元的差，则该上界为5，且两个上界均是最优的。我们还给出了存在非零两两Jordan乘积的无限集，以及由非奇异矩阵构成的无限集的充要条件。
英文摘要
Let $U$ be the ring of upper triangular $2\times2$ integer matrices. For $N\in U$, a Jordan $D(N)$-set is a set of distinct nonzero matrices in $U$ such that $(AB+BA)/2+N$ is a square in $U$ for any two distinct elements $A$ and $B$. We determine all $N$ for which an infinite Jordan $D(N)$-set exists. If no infinite set exists, every such set has at most six elements. If $N$ is not a difference of two squares in $U$, the bound is five. Both bounds are best possible. We also give necessary and sufficient conditions for the existence of infinite sets with nonzero pairwise Jordan products and of infinite sets consisting of nonsingular matrices.
