Sentence:  The definition of <WSD>p-adic norm</WSD> should obey the usual conditions, in particular the requirement that the norm of product is product of norms. 
Meaning of the word marked with <WSD> tags:  A "p"-adic absolute value, for a given prime number "p", the function, denoted |..|<sub>p</sub> and defined on the rational numbers, such that |0|<sub>p</sub> = 0 and, for "x"≠0, |"x"|<sub>p</sub> = "p"-ord<sub>"p"</sub>("x"), where ord<sub>"p"</sub>("x") is the "p"-adic ordinal of "x";<ref>'''2011''', Andrew Baker, [http://www.maths.gla.ac.uk/~ajb/dvi-ps/padicnotes.pdf An Introduction to "p"-adic Numbers and "p"-adic Analysis], Definition 2.5</ref> the same function, extended to the "p"-adic numbers ℚ<sub>"p"</sub> (the completion of the rational numbers with respect to the "p"-adic ultrametric defined by said absolute value); the same function, further extended to some extension of ℚ<sub>"p"</sub> (for example, its algebraic closure).