A weak cancellation property for monoids

An example. Consider the set $\{n\mid n\gt 0\}\cup \{u_n \mid n\gt 0\}\cup\{0\}$ with operation + which is the usual + on natural numbers, $n+u_k=u_k+n=(n+k), u_k+u_n=u_{k+n}$, $0+x=x+0=x$ for every $x$. It is a commutative non-cancelative monoid satisfying your condition. I do not think this class of monoids has a name.

There are books on commutative semigroups (Redei, Grillet,...).

Tags:

Abstract Algebra

Monoid

Related

How can I find real, symmetric matrices $A,B$ such that $Ax =\lambda B x $ has no real eigenvalues and eigenvectors? Is it possible to solve $\frac{dy}{dx}=y^x$? Is Fodor's Lemma necessary for the $\omega_1$ train station puzzle? Completing the proof using strong induction for $E = \bigcap_{n=1}^\infty E_n $ What are all possible positive integers $k$ such that $k=\frac{a^2+b^2+c^2}{bc+ca+ab}$ for some positive integers $a$, $b$, and $c$? Struggling to Understand Algorithm for Displaying Polynomial Matings with Julia Sets Why is $ \frac{5}{64}((161+72\sqrt{5})^{-n}+(161+72\sqrt{5})^{n}-2)$ always a perfect square? What's a fair way to share fees in a group road trip with a personal and a rental car? Explain why the characteristic curves generate the solution surface $\cos\theta\cos2\theta\cos3\theta + \cos2\theta\cos3\theta\cos4\theta + ...$ All solutions of $f(x)f(-x)=1$ Does $\partial A$ determine $A$?

Recent Posts