All Questions
Tagged with magma binary-operations
25
questions
2
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0
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26
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Conservative idempotent magma - proof attempt
I need help with checking proof about idempotent and conservative magmas.
Let magma be any ordered pair $(M, \odot)$, where $M$ is nonempty set and $\odot$ binary operation on $M$.
Now I need to ...
0
votes
1
answer
20
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Maximal Extension Chain of Halfgroupoids
A book I am reading gives the following definitions:
A collection $\{L_i:i=0,1,2,...\}$ of halfgroupoids $L_i$ is called an extension chain if $L_{i+1}$ is an extension of $L_i$ for each $i$. If $G$ ...
- 31
0
votes
0
answers
34
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Closest Equivalent to Cayley Graphs for Partial Groupoids?
[A partial groupoid (half-magma) is a set S equipped with a (single-valued) partial binary operation, as in Bruck's Survey of Binary Systems.]
This question may be nonsensical, given that the duality ...
- 31
1
vote
0
answers
78
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non-commutative algebraic structure with 16 elements, need help categorizing it and finding a representation
We have an abstract algebraic structure with the following multiplication table, has anyone seen this structure before and can anyone give it a proper name and a simple (possibly matrix) ...
- 21
1
vote
1
answer
118
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if $\cdot$ and $\odot$ are associative operations on $\mathbb{Z}$ when is the sum $(\cdot + \odot)$ associative?
Where $a(\cdot + \odot)b$ is defined as $(a\cdot b) + (a\odot b)$.
I know if $\cdot$ and $\odot$ distribute through addition (i.e. $a\cdot(b+c)=a\cdot b+ a\cdot c$) then the sum $(\cdot + \odot)$ is ...
- 822
7
votes
2
answers
466
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If not associative, then what?
Consider a binary operation $*$ acting from a set $X$ to itself. It's useful and standard to work with operations which are associative, such that $(a*b)*c = a*(b*c)$. What about operations which are ...
- 1,324
2
votes
1
answer
238
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Fill in a partly filled in table such that it makes the magma $(M,*)$ associative, commutative, has an identity element and has no zero-elements.
Below is a partly filled in table for a binary operation ($*$) on the set $M=\{a,b,c,d\}$. I am trying to fill in the rest such that the magma $(M,*)$ becomes associative, commutative, has an identity ...
- 417
1
vote
1
answer
408
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What is the identity element of 4
If $*$ is a binary operation taking the greater of two distinct numbers, construct a table for the operation on the set $S=\{1,2,3,4,5\}$. What is the identity element of 4? Is the operation ...
- 11
1
vote
1
answer
258
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All magmas of order n (specifically 3)
I am considering the collection of all magmas (sets with binary operations) of order 3. Since we just need a binary operation and no other properties, it makes sense to define a magma in terms of all ...
- 1,681
0
votes
1
answer
88
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Uniqueness of two side zeroes of binary operation
I came across the following fact in group theory:
Two-sided identity of binary operation is unique.
Does the similar statement for two sided zero also holds? :
Two-sided zero of binary ...
- 1,317
4
votes
1
answer
349
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Is there a name for an algebraic structure with only "addition" and "truncated subtraction"?
Given a set $S$ with
An associative binary "addition" operation $+$ with corresponding neutral element $0$ such that $(S, +)$ is a monoid
A non-associative binary "truncated subtraction" operation $-$...
- 1,145
5
votes
3
answers
199
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Terminology: Semigroups, only their "binary operations" aren't closed.
Motivation:
Consider $\mathcal{X}=(X, +)$, where $X=\{-1, 0, 1\}$ and $+$ is standard addition. Then $\mathcal{X}$ is associative (where defined) but not closed.
NB: There is an identity element in $X$...
- 45.8k
8
votes
2
answers
232
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Structures with $x*(y*z) = y*(x*z)$
In reading http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=182143561104878BDABB72258DA254D0?doi=10.1.1.18.2521&rep=rep1&type=pdf , they mentioned an interesting relation -- they had a ...
- 2,503
0
votes
1
answer
198
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Group Theory For an algebraic system, how to prove the following?
I'm trying to prove the below equation
(From Elements of discrete mathematics, second edition by C. L. Liu
Question 11.13)
Let $(A, +)$ be an algebraic system such that for all $a, b$ in $A$ we ...
- 11
2
votes
1
answer
142
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Sufficient condition for a magma to be a topological magma
Let $(B,\ast)$ be a magma (that is, $\ast:B\times B\to B$ is a binary operation on $B$), and let $\tau$ be a topology on $B$. If $X$ is any set and we define $\tilde\ast$ in the set $B^X$ of functions ...
- 6,131