HOMEWORKS
Homework 2
Following the pattern in definitions of isomorphism of groups, rings, etc.,
give the definition of isomorphism of
orders. How
many non-isomorphic orders are there on the set of 3 elements?
Homework 4
Is it true that any semigroup consisting of a) 1 element b) 2 elements, is a
group?
List of semigroups consisting of 2 elements.
Homework 5
Let \(K\) be a field, and
\(X\) and \(Y\) are two sets such that \(K[X] \simeq K[Y]\) (recall that \(K[X]\) is the polynomial
algebra with the set \(X\) as indeterminates). Prove that \(X\) and \(Y\) have the
same cardinality.
Try to find a proof using the universal property of polynomial
algebras.
Such proof is not possible.
Created: Thu Sep 23 2021
Last modified: Tue Nov 8 18:14:48 CET 2022