Abstract
Rings and distributive lattices are semirings with regular and commutative addition, whence they can be regarded as semirings equipped with the unary operation of additive inversion. We shall show that within this framework the least variety containing all rings and distributive lattices is the variety of "semirings which are lattices of rings" in the sense of Bandelt and Petrich [1]. The proof of this is based on a description of the free objects in the latter variety.
Research partially supported by NSERC Grant A 2985
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References
H.-J. Bandelt and M. Petrich, Subdirect products of rings and distributive lattices, Proc. Edinburgh Math. Soc. 25 (1982), 155–171.
G. Grätzer, Universal algebra, 2nd ed., Springer-Verlag, 1979.
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© 1983 Springer-Verlag
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Bandelt, HJ. (1983). Free objects in the variety generated by rings and distributive lattices. In: Hofmann, K.H., Jürgensen, H., Weinert, H.J. (eds) Recent Developments in the Algebraic, Analytical, and Topological Theory of Semigroups. Lecture Notes in Mathematics, vol 998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062034
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DOI: https://doi.org/10.1007/BFb0062034
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