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In a finite monoid (M, $\circ$) if the identity element $e$ is the only idempotent element, prove that each element of the monoid is invertible.

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#abstract-algebra #group-theory #monoid #binary-operations #quasigroups
167
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Up to what level can associativity be guaranteed?

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#group-theory #associativity #cayley-table #quasigroups
52
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Invertibility as Criteria for a Loop

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#abstract-algebra #divisibility #inverse #magma #quasigroups
385
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Commutative subtraction

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#abstract-algebra #abelian-groups #semigroups #magma #quasigroups
192
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Definition of Additive Loop

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#abstract-algebra #terminology #binary-operations #quasigroups
99
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Multiplication table of a commutative quasigroup is a symmetric latin square. Is the converse also true?

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#latin-square #quasigroups
39
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Why quasi-random sequences are generated in the interval [0,1]? Is it a normalized sequence generation?

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#sequences-and-series #algorithms #random #algorithmic-randomness #quasigroups
928
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The smallest quasigroup which is not a group

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#abstract-algebra #group-theory #quasigroups
2.9k
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Examples of quasigroups with no identity elements

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#abstract-algebra #examples-counterexamples #quasigroups
534
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Identifying all the quasigroups of order $3$ up to isomorphism

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#abstract-algebra #quasigroups
54
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How can one construct a strict quasigroup with neither a left nor a right identity on $n$ elements?

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#abstract-algebra #quasigroups
107
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What are some examples of infinite strict quasigroups?

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#abstract-algebra #examples-counterexamples #quasigroups
23
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Imbedding in the quasi-group

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#quasigroups
91
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All loops of order less than $5$ are groups

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#abstract-algebra #quasigroups
90
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Property of normal subloops

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#abstract-algebra #universal-algebra #quasigroups

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