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cummings12332
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Homework Statement
Is (x^2-1) a unit in F[x]? where F is a field.
2. The attempt at a solution
I might say yes, cause we can find the taylor expansion of 1/(x^2-1), is my idea right?
cummings12332 said:Homework Statement
Is (x^2-1) a unit in F[x]? where F is a field.
2. The attempt at a solution
I might say yes, cause we can find the taylor expansion of 1/(x^2-1), is my idea right?
A unit in a ring is an element that has a multiplicative inverse in the ring. In other words, when multiplied by another element, the result is the identity element of the ring.
A zero divisor is an element in a ring that when multiplied by another element, the result is zero. A unit, on the other hand, has a multiplicative inverse and cannot be a zero divisor.
No, not all elements in a ring are units. Only elements that have a multiplicative inverse are considered units.
No, a unit can only have one multiplicative inverse in a ring. If an element has more than one inverse, then it is not considered a unit.
A unit in a ring is an element that has a multiplicative inverse in the ring, whereas a unit in a group is an element that has an inverse under the group's operation. In other words, a unit in a ring is a special case of a unit in a group.