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Titlebook: Semirings and their Applications; Jonathan S. Golan Book 1999 Springer Science+Business Media Dordrecht 1999 Algebra.Computer.computer sci

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Building New Semirings from Old,notation” for such matrices. We have already noted that addition of such matrices, defined componentwise, turns ... into a commutative additive monoid, the identity element of which is the function which takes every element of . × . to 0.
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Additively-Regular Semirings,ent ... satisfies both of the above conditions. If a ∈ ... then . is additively regular with .... If . is a congruence relation on . and . is an additively-regular element of . then surely . is an additively-regular element of ..
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Semimodules over Semirings,etting. Moreover, many important constructions in pure and applied mathematics can, as we shall see, be understood as semimodules over appropriate semirings. In this chapter we lay the foundations for the study of semimodules.
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