MathDB

a)Is it true that for every non-empty set

A

and every associative operation

*:A \times A \to A

the conditions

x*x*y=y \;\;\; \text{and}\; \;\; y*x*x=y

for every

x,y\in A

imply commutativity of

*

?
b)a)Is it true that for every non-empty set

A

and every associative operation

*:A \times A \to A

the condition

x*x*y=y

for every

x,y\in A

implies commutativity of

*

?
Proposed by Paulius Drungilas, Arturas Dubickas (Vilnius University).

Problem Statement