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Orderpotentf-rings

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Abstract

The class off-rings in which the product of anyn elements is comparable to zero (n-order-potentf-rings) generalizes the concept of both totally ordered and nilpotentf-rings. Necessary and sufficient conditions are found for anf-ring to ben-orderpotent. It is shown thatn-orderpotency is closely related to the ring having sufficiently many annihilating elements. Special consideration is given to generalized semigroup rings, a rich source of examples.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Texas at El Paso, 79968, El Paso, TX, USA

    A. M. Duval & P. J. Wojciechowski

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  1. A. M. Duval
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  2. P. J. Wojciechowski
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Dedicated to the memory of Alan Day

Parts of this paper based on this author's doctoral dissertation under the direction of Professor W. Charles Holland at Bowling Green State University.

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Duval, A.M., Wojciechowski, P.J. Orderpotentf-rings. Algebra Universalis 34, 510–526 (1995). https://doi.org/10.1007/BF01181875

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  • DOI: https://doi.org/10.1007/BF01181875

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