topologia del maxim comú divisor

E_{j} = k^{j}
¬E_{j} = (1/k^{j})


mcd{k^{m},...,k^{n}}=k^{m} & [Aj][ k^{m}·k^{j+(-m)} = k^{j} ]
mcm{k^{m},...,k^{n}}=k^{n} & [Aj][ k^{j}·k^{n+(-j)} = k^{n} ]


mcd{(1/k^{m}),...,(1/k^{n})}=(1/k^{n}) & [Aj][ (1/k^{n})·k^{n+(-j)} = (1/k^{j}) ]
mcm{(1/k^{m}),...,(1/k^{n})}=(1/k^{m}) & [Aj][ (1/k^{j})·k^{j+(-m)}=(1/k^{m}) ]