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April 10th, 2014, 08:45 PM  #1 
Newbie Joined: Apr 2014 From: Pune, India Posts: 1 Thanks: 0  Name for a kind of set
Hi, I came across a problem that is solved by using set with the following properties Set S is an abelian semigroup under an operation (say +) Set S is an semigroup under an operation (say .) operation . is distributive over +. i.e. if a, b, c are members of set S, then a.(b+c) = (a.b) + (a.c) Is there a name for this kind of a set? 
April 13th, 2014, 06:56 PM  #2 
Senior Member Joined: Mar 2012 Posts: 294 Thanks: 88 
If it had a 0, and a 1, it would be a semiring. Some authors also use this term for semirings that do not possess a multiplicative identity, and some do not even require a 0: compare: Semiring  Wikipedia, the free encyclopedia Semiring  from Wolfram MathWorld If we require the distributivity just be onesided, but still have a 0, which in addition is an "absorbing element" (0.a = 0, or a.0 = 0, depending on "which sidedness we have") we have a nearsemiring. Many of these structure arise as certain kinds of functions, or by considering structures based on the natural numbers. 

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