In the mid-1970s, famous American homological algebra and commutative algebra mathematician Maurice Auslander (August 3, 1926 - November 18, 1994) introduced the Auslander algebra.
Ever since, the concept has been widely used in the algebra branch of mathematics.
Basically, the Auslander algebra of an algebra A is the endomorphism ring of the total of the indecomposable modules of A.
Field
Variable
Natural number
Kepler value
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Variable
Trigonometric value
Time
Valency
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Γ ≤ 2
Γ = 2
Γ < 2
Γ > 2
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Endomorphism ring
Exomorphism ring
Static ring
External ring
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If the projective dimension of its socle does not exceed one
If the projective dimension of its socle is more than one
If the projective dimension of its socle is between 1 and -1
If the projective dimension of its socle equals to one tÂ
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Real number
Whole number
Natural number
Constant number
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Exceeds 1
Less than -1
Does not exceed 1
More than -1
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Aqua-hereditary
Quasi hereditary
Hereditary
Non-hereditary
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Decomposable modules
Incompressible modules
Normal modules
Indecomposable modules
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If the projective dimension of its socle does not exceed one
If the projective dimension of its socle is more than one
If the projective dimension of its socle is between 1 and -1
If the projective dimension of its socle equals to one t
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