Ztartománybeli

Ztartománybeli is a term used in mathematics, specifically within abstract algebra, to describe a property of rings. A ring R is said to have the Ztartománybeli property if every non-zero zero-divisor is a unit. A zero-divisor in a ring R is a non-zero element 'a' such that there exists another non-zero element 'b' in R where either ab = 0 or ba = 0. A unit in a ring is an element that has a multiplicative inverse. Therefore, if a ring is Ztartománybeli, then any element that can "annihilate" another non-zero element must itself be invertible.

This property is closely related to the concept of integral domains. An integral domain is a commutative ring with unity and no zero-divisors. If a commutative ring with unity is Ztartománybeli, it is equivalent to being an integral domain. The presence of zero-divisors that are not units means the ring is not an integral domain. The Ztartománybeli property focuses on the nature of these zero-divisors, requiring them to be units, which implies a certain level of regularity within the ring's structure. Examples of rings with the Ztartománybeli property include fields, as all non-zero elements in a field are units and there are no zero-divisors.