A Combinatorial Commutativity Property for Rings
نویسندگان
چکیده
Clearly, every commutative ring is a Qn-ring for arbitrary n; moreover, there exist badly noncommutative Qn-rings, since every ring with fewer than n elements is a Qnring. Our purpose is to identify conditions which force Qn-rings to be commutative or nearly commutative. It is obvious that every Qn-ring is a Pn-ring and every Pn-ring is a P∞-ring. We make no use of the results on Pn-rings in [1], and most of our results are of a different sort than those in [1]. However, a special case of the theorem on P∞-rings in [2] plays a crucial role in our study.
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