My Math Forum  

Go Back   My Math Forum > College Math Forum > Abstract Algebra

Abstract Algebra Abstract Algebra Math Forum

Thanks Tree1Thanks
  • 1 Post By Deveno
LinkBack Thread Tools Display Modes
April 10th, 2014, 08:45 PM   #1
Joined: Apr 2014
From: Pune, India

Posts: 1
Thanks: 0

Name for a kind of set


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?
debasish is offline  
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 semi-ring. Some authors also use this term for semi-rings that do not possess a multiplicative identity, and some do not even require a 0:

Semiring - Wikipedia, the free encyclopedia
Semiring -- from Wolfram MathWorld

If we require the distributivity just be one-sided, 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 near-semiring.

Many of these structure arise as certain kinds of functions, or by considering structures based on the natural numbers.
Thanks from Olinguito
Deveno is offline  

  My Math Forum > College Math Forum > Abstract Algebra

kind, names, set

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
What Kind Of Math Is This? Zadok Economics 1 December 13th, 2012 10:36 AM
What Kind of Math is This? Jabby J New Users 3 October 15th, 2011 08:09 PM
What kind of problem is this? aloe Advanced Statistics 3 October 11th, 2011 02:11 PM
Help! What kind of function is this? rmaier9 Applied Math 3 August 26th, 2011 04:09 AM
Three of a kind kaaib Algebra 2 May 10th, 2009 02:01 PM

Copyright © 2019 My Math Forum. All rights reserved.