0 votes 0 votes Is this monoid: Addition modulo (take mode using m) on the set of Integers (Z m)={0,1,2,3,4,…..m-1} i.e. For all a a (+ modulo using m) e = e (+ modulo using m) a =a here, e is an identity element Set Theory & Algebra group-theory discrete-mathematics + – Nandkishor3939 asked Jan 13, 2019 Nandkishor3939 862 views answer comment Share Follow See all 10 Comments See all 10 10 Comments reply Kunal Kadian commented Jan 13, 2019 reply Follow Share It is a Monoid, bcoz there exist identity $e= 0$ Infact it is a group... Moreover an Abelian group. 0 votes 0 votes srestha commented Jan 13, 2019 reply Follow Share @Kunal Kadian what is inverse element if it is group? 0 votes 0 votes Kunal Kadian commented Jan 13, 2019 reply Follow Share @srestha For any element a, inverse b = (m-a) mod m 0 votes 0 votes Nandkishor3939 commented Jan 13, 2019 reply Follow Share Can The Identity element be m 0 votes 0 votes Kunal Kadian commented Jan 13, 2019 reply Follow Share @Nandkishor3939 I think idenitity element should belong to the given set, m is not in given set. Moreover identity element, if exists, is unique. here it is $0$ 0 votes 0 votes srestha commented Jan 13, 2019 reply Follow Share yes, 0 is identity element and inverse of any element w.r.t. 0 I mean 1 has inverse of 4 right? that is why group 0 votes 0 votes Kunal Kadian commented Jan 13, 2019 reply Follow Share @srestha Yes, If you take m= 5, then inverse of 1 is 4. For any general case, inverse of 1 = m-1 0 votes 0 votes Nandkishor3939 commented Jan 13, 2019 reply Follow Share a (+ modulo using m) m = m (+ modulo using m) a =a As m donot belong to our set so it is not e right? 0 votes 0 votes Kunal Kadian commented Jan 14, 2019 reply Follow Share Yea Right. 0 votes 0 votes InsaneMockingBird commented Dec 29, 2019 reply Follow Share This is additive modulo and given is set of intergers. Hence, Inverse of every element will be same negative number 0 votes 0 votes Please log in or register to add a comment.