Editing I-adic topology (section)

==Definition==
Let {{mvar|R}} be a commutative ring and {{mvar|M}} an {{mvar|R}}-module. Then each [[ideal (ring theory)|ideal]] {{math|𝔞}} of {{mvar|R}} determines a topology on {{mvar|M}} called the {{math|𝔞}}-adic topology, characterized by the [[pseudometric space|pseudometric]] <math display=block>d(x,y) = 2^{-\sup{\{n \mid x-y\in\mathfrak{a}^nM\}}}.</math>  The family <math display=block>\{x+\mathfrak{a}^nM:x\in M,n\in\mathbb{Z}^+\}</math> is a [[basis (topology)|basis]] for this topology.{{sfn|Singh|2011|p=147}}

An {{math|𝔞}}-adic topology is a [[linear topology]] (a topology generated by some submodules).<!-- but the converse is false, I think -->