Left and right invariance in an integral domain

Beauregard, Raymond A.

doi:10.1090/S0002-9939-1977-0457480-2

Left and right invariance in an integral domain
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by Raymond A. Beauregard PDF

Proc. Amer. Math. Soc. 67 (1977), 201-205 Request permission

Abstract:

A ring is said to be right (left) invariant if each of its right (left) ideals is twosided. In this paper we resolve the conjecture: Every right invariant integral domain which satisfies the left Ore (multiple) condition is left invariant. A proof is given for the class of LCM domains satisfying a finiteness condition. An example is given to show that the LCM hypothesis cannot be dropped. A second example shows that the conjecture fails even in a Bezout domain which does not have the finiteness condition. The problem of right versus left boundedness is also considered.

References

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