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Special classes of l-rings

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Abstract

We study a special class of lattice-ordered rings and a special radical. We prove that a special radical of an l-ring is equal to the intersection of the right l-prime l-ideals for each of which the following condition holds: the quotient l-ring by the maximal l-ideal contained in a given right l-ideal belongs to the special class. The prime radical of an l-ring is equal to the intersection of the right l-semiprime l-ideals. We introduce the notion of a completely l-prime l-ideal. We prove that N 3(R) is equal to the intersection of the completely l-prime, right l-ideals of an l-ring R, where N 3(R) is the special radical of the l-ring R defined by the class of l-rings without positive divisors of zero.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    N. E. Shavgulidze

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  1. N. E. Shavgulidze
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Correspondence to N. E. Shavgulidze.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 1, pp. 157–173, 2009.

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Shavgulidze, N.E. Special classes of l-rings. J Math Sci 166, 794–805 (2010). https://doi.org/10.1007/s10958-010-9896-y

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  • DOI: https://doi.org/10.1007/s10958-010-9896-y

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