41. I believe I erroneously thought that this then would imply that the quasigroup has an identity element . 42. Note that a group is in particular a pointed set, with the identity element as distinguished point. 43. When speaking of the one ( see empty product ), since one is the identity element for multiplication. 44. Up to equivalence of extensions, the Baer sum is commutative and has the trivial extension as identity element . 45. Quasigroup homomorphisms necessarily preserve left and right division, as well as identity elements ( if they exist ). 46. Consequently, the speech community increased as well and Minderico became to be seen as a unifying identity element . 47. For example, it is immediately proven from the axioms that the identity element of a group is unique. 48. From the definition of a monoid, one can show that the identity element " e " is unique. 49. The process of adjoining an identity element to a rng can be formulated in the language of category theory. 50. So for any particular pair ( M, V ) there exists an identity element P for the symplectic sum.
