The June Meeting in Portland
نویسنده
چکیده
s of papers presented at the meeting follow. Abstracts whose titles are followed by "t" were presented by title. Mrs. Lehmer was introduced by the Associate Secretary, Mr. Rail by Professor Lonseth, Professor Nash by Professor W. T. Martin, and Mr. Krabble by Professor C. B. Morrey. ALGEBRA AND THEORY OF NUMBERS 5SSt. W. E. Barnes: Primal ideals in noncommutative rings. In any associative ring R an element x is not right prime (nrp) to an ideal A . if yRxÇ^A for some y ^A. An ideal is primal if the elements nrp to it form an ideal. These definitions differ from those of Curtis (Amer. J. Math. vol. 76 (1952) pp. 687700) but reduce to them for rings with unit and A.C.C. for ideals. They also reduce to Fuchs' (Proc. Amer. Math. Soc. vol. 1 (1950) pp. 1-8) for commutative rings. An ideal B is nrp to A if every element of B is nrp to A. Maximal nrp to A ideals always exist and their intersection is called the adjoint of A. In a class of rings, called uniform, the maximal nrp ideals of any ideal are prime. The A.C.C. implies uniformity, but not conversely. Results (similar to the classical Noether theory) on representations of an ideal as the intersection of primal ideals with prime adjoints are obtained which include those of Fuchs and Curtis. (Received May 3, 1954.) 589. W. E. Barnes: Principal component ideals in noncommutative
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Report on First Iranian International Conference on Women’s Health Held June 14-15, 2012 in Shiraz, Iran
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