Category:Examples of Tidy Factorizations
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This category contains examples of Tidy Factorization.
Let $\struct {D, +, \circ}$ be an integral domain whose unity is $1_D$.
Let $\struct {U_D, \circ}$ be the group of units of $\struct {D, +, \circ}$.
Any factorization of $x \in D$ can always be tidied into the form:
- $x = u \circ y_1 \circ y_2 \circ \cdots \circ y_n$
where $u \in \struct {U_D, \circ}$, and may be $1_D$, and $y_1, y_2, \ldots, y_n$ are all non-zero and non-units.
This is done by forming the ring product of all units of a factorization into one unit, and rearranging all the remaining factors as necessary.
Such a factorization is called tidy.
Pages in category "Examples of Tidy Factorizations"
The following 2 pages are in this category, out of 2 total.