Let \({{\mathfrak {J}}}\, \) and \({{\mathfrak {J}}}\, ^{'}\) be Jordan rings. In this paper we study the additivity of n-multiplicative isomorphisms from \({{\mathfrak {J}}}\, \) onto \({{\mathfrak {J}}}\, ^{'}\) and of n-multiplicative derivations of \({{\mathfrak {J}}}\, \). Suppose that \({{\mathfrak {J}}}\, \) contains a nontrivial idempotent; we prove that if \({{\mathfrak {J}}}\, \) satisfying certain conditions, then n-multiplicative maps and n-multiplicative derivations from \({{\mathfrak {J}}}\, \) to \({{\mathfrak {J}}}\, ^{'}\) are additive maps.

令\（{{\ mathfrak {J}}} \，\）和\（{{\ mathfrak {J}}} \，^ {'} \）为Jordan环。在本文中，我们研究了从\（{{\ mathfrak {J}}} \，\）到\（{{\ mathfrak {J}}} \\，^ {'} \）和的n个乘法同构的可加性\（{{\ mathfrak {J}}} \，\）的n乘导数。假设\（{{\ mathfrak {J}}} \，\）包含一个非平凡的幂等；我们证明，如果\（{{\ mathfrak {J}}} \，\）满足特定条件，则从\（{{\ mathfrak {J}}} \，\）到n的n个乘法映射和n个乘法\（{{\ mathfrak {J}}} \，^ {'} \）是累加图。