A nonzero element of a free abelian group is primitive when it is part of an integral basis, equivalently when some homomorphism to takes it to one. Its coordinates have greatest common divisor one. This lattice meaning differs from a primitive homology class in the coalgebra sense.
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A **free abelian group** is a specific type of mathematical structure in the field of group theory. To understand it, let's break down the terminology: 1. **Group**: A group is a set \( G \) equipped with a binary operation (often called multiplication) that satisfies four properties: closure, associativity, identity, and invertibility.