User:CJKG/Eigenbox: Difference between revisions
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a) <math>\mathcal{M}</math> is called '''right-equiponent magma''' or '''R-equiponent magma''' if and only if | a) <math>\mathcal{M}</math> is called '''right-equiponent magma''' or '''R-equiponent magma''' if and only if | ||
<math>\exists M, \circ</math> with <math>((M; \circ) = \mathcal{M} \wedge \circ: M \times M \to M)</math> such that | <math>\exists M, \circ</math> with <math>((M; \circ) = \mathcal{M} \wedge \circ: M \times M \to M)</math> such that | ||
<math>\forall a \in M \exists b \in M \forall c \in M (c \circ a) \circ c = b</math> (''R-equiponency law''). | <math>\forall a \in M \exists b \in M \forall c \in M (c \circ a) \circ c = b</math> (''R-equiponency law''). | ||
b) <math>\mathcal{M}</math> is called '''left-equiponent magma''' or '''L-equiponent magma''' if and only if | b) <math>\mathcal{M}</math> is called '''left-equiponent magma''' or '''L-equiponent magma''' if and only if | ||
<math>\exists M, \circ</math> with <math>((M; \circ) = \mathcal{M} \wedge \circ: M \times M \to M)</math> such that | <math>\exists M, \circ</math> with <math>((M; \circ) = \mathcal{M} \wedge \circ: M \times M \to M)</math> such that | ||
<math>\forall a \in M \exists b \in M \forall c \in M c \circ (a \circ c) = b</math> (''L-equiponency law''). | <math>\forall a \in M \exists b \in M \forall c \in M c \circ (a \circ c) = b</math> (''L-equiponency law''). | ||
Remark: <math>M = \emptyset</math> is allowed. | Remark: <math>M = \emptyset</math> is allowed. | ||
c) <math>\mathcal{M}</math> is called '''column-preserving''' if and only if <math>\mathcal{M}</math> is a magma and | |||
<math>\exists M, \circ</math> with <math>(M; \circ) = \mathcal{M}</math> such that | |||
<math>\forall a, b \in M b \circ (b \circ a) = a</math> (''column-preserving law''). | |||
d) <math>\mathcal{M}</math> is called '''row-preserving''' if and only if <math>\mathcal{M}</math> is a magma and | |||
<math>\exists M, \circ</math> with <math>(M; \circ) = \mathcal{M}</math> such that | |||
<math>\forall a, b \in M (a \circ b) \circ b = a</math> (''row-preserving law''). | |||
e) A magma <math>(M;\circ)</math> is called '''static''' <math>: \leftrightarrow</math> | |||
<math>\forall a \in M \exists b \in M \forall c \in M a \circ (b \circ c) = c</math> (''staticity law''). | |||
Revision as of 12:35, 19 July 2014
a) is called right-equiponent magma or R-equiponent magma if and only if with such that
(R-equiponency law).
b) is called left-equiponent magma or L-equiponent magma if and only if with such that
(L-equiponency law).
Remark: is allowed.
c) is called column-preserving if and only if is a magma and with such that
(column-preserving law).
d) is called row-preserving if and only if is a magma and with such that
(row-preserving law).
e) A magma is called static
(staticity law).
