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What does non-zero factor mean?
A non-zero factor is an element in a ring (or domain) that is not equal to zero and has no zero factor.

In abstract algebra, a ring is a set, which is equipped with two binary operations (addition and multiplication) and satisfies some properties. In a ring, non-zero factors refer to elements other than zero, and the result of their multiplication with other non-zero elements is not zero. In other words, if elements A and B in a ring satisfy ab≠0, a≠0 and b≠0, then both A and B are called non-zero factors. Non-zero factors have important properties and applications in ring theory and algebra. They play a key role in understanding and studying the structure, ideal, prime element and unique decomposition of rings. The concept of non-zero factor is also related to divisibility, which can be used to define and describe algebraic structures such as whole rings, fields and integers.