Additively-Regular Semirings

Jonathan S. Golan
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Jonathan S. Golan: University of Haifa

Chapter 13 in Semirings and their Applications, 1999, pp 143-147 from Springer

Abstract: Abstract An element a of a semiring R is additively regular if and only if there exists an element a # of R satisfying a + a + a # = a and e # + a # + a = a # . Actually, as in the case of multiplicatively-regular elements, it suffices to assume that there exists an element b of R satisfying a + a + b = a for, if such an element exists, the element a # = b + b + a satisfies both of the above conditions. If a ∈ I + (R) then a is additively regular with a # = a. If p is a congruence relation on R and a is an additively-regular element of R then surely a/p is an additively-regular element of R/ρ.

Date: 1999
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DOI: 10.1007/978-94-015-9333-5_13

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