x1=t2 is an element in the set that underlies structure/ring x2≈s3 that is nilpotent in that structure with nilpotency x3=t3 (nonnegative integer according to the typical rules)

x3 is the minimum positive exponent such that x1 multiplied by itself that many times (according to the definition of multiplication imposed by and endowing structure x2) is identically the zero(-like) element in that structure; any greater power will likewise be zero(-like). The zero(-like) element is itself trivially nilpotent with nilpotency 1. Warning: This word is for nilpotent elements. Nilpotent groups, for example, should not be referred to by this word except when considered as whole objects that participate as elements in some larger structure. See also: nonsmi