Let $(\{p,q\},∗)$ be a semigroup, where $p∗p=q$. I want to show that:
$$q∗q=q$$
I know semigroups are closed and associative, but I am not able to prove this equality.
2026-03-25 06:09:03.1774418943
A question about a semigroup with two elements
124 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ABSTRACT-ALGEBRA
- Feel lost in the scheme of the reducibility of polynomials over $\Bbb Z$ or $\Bbb Q$
- Integral Domain and Degree of Polynomials in $R[X]$
- Fixed points of automorphisms of $\mathbb{Q}(\zeta)$
- Group with order $pq$ has subgroups of order $p$ and $q$
- A commutative ring is prime if and only if it is a domain.
- Conjugacy class formula
- Find gcd and invertible elements of a ring.
- Extending a linear action to monomials of higher degree
- polynomial remainder theorem proof, is it legit?
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
Related Questions in SEMIGROUPS
- What concept does a natural transformation between two functors between two monoids viewed as categories correspond to?
- Question about semigroups of permutations
- Isomorphism between finitely generated semigroups
- a question on Ellis semigroup
- Semigorup variety, hyperassociativity,idempotentunclear proof of $x^4\approx x^2$
- Hyperidentity, semigroups, bands.
- Maximal subgroup of a finite semigroup (GAP)
- Hypersubstitution, m-ary terms, semigroups, equivalent definitions
- Direct product of two finite monogenic semigroup
- Properties of infinite semigroup
Related Questions in IDEMPOTENTS
- Prove that an idempotent element must be either 0, 1 or a zero-divisor.
- What is the set {$e\in(R/ I)\times(R/J): e$ is idempotent}
- The idempotent elements of Eisenstein Integers
- Prove that $A-I_n$ is idempotent
- Idempotent substitution $\theta$
- Relations of structures related to conjugate idempotents
- Composition series of regular module
- Is $A^3=A$ a condition for idempotency of matrices?
- Is it true that $X(X'X)^{-1}X'-J/n$ is idempotent, where $J$ is an $n$ by $n$ matrix of ones?
- Idempotents over a ring with zero divisors
Related Questions in FINITE-SEMIGROUPS
- Inclusion relations between equationally defined classes of finite semigroups
- make me idempotent!
- Semigroup of differentiable functions on real line
- isomorphism generalized semigroup
- Implicit operations in finite semigroups.
- Right zero in a finite semigroup
- Is the inverse image of a group also a group for semigroup homomorphisms
- Equal nr of $\mathscr D$-classes, different nr of idempotents
- Subsemigroup of a finite simple semigroup is simple
- Period of semigroup
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Hint:
Suppose to the contrary that $q*q=p$.
Case 1: $p*q=p$. Try to derive a contradiction thinking about $p*p*q$.
Case 2: $p*q=q$. Same advice as case 1.