This article will use " quotient von Neumann regular " to refer to this type of regular ideal.
2.
In commutative algebra a "'regular ideal "'refers to an ideal containing a non-zero divisor.
3.
As a consequence of this lemma, it is apparent that every ideal of a von Neumann regular ring is a von Neumann regular ideal.
4.
An example of a noncompact, finite volume hyperbolic manifold obtained in this way is the Gieseking manifold which is constructed by glueing faces of a regular ideal hyperbolic tetrahedron together.
5.
He showed that the figure-eight knot complement could be decomposed as the union of two regular ideal hyperbolic tetrahedra whose hyperbolic structures matched up correctly and gave the hyperbolic structure on the figure-eight knot complement.
6.
An ideal \ mathfrak { i } is called a ( von Neumann ) regular ideal if it is a von Neumann regular non-unital ring, i . e . if for every element " a " in \ mathfrak { i } there exists an element " x " in \ mathfrak { i } such that.
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