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Some observations:
The following markup will center all text content with the DIV, even content found within a table (unless the table's cells are given explicit value for the attribute align or the property text-align).
This happens because a strict DOCTYPE claims that the document is authored according to a strict adherence to the W3C specification. Upon seeing this, IE6 will kick its rendering engine into strict mode, so that the document will be displayed according to the W3C standards. This affects the browser's handling of both CSS and HTML. Since "text-align" according to CSS2 is inherited, tables inside the DIV will have their content centered in standard compliant browsers in strict mode. If you don't declare the alignment for individual elements, they will take the inherited alignment. The actual cause of this rendering in Internet Explorer 6 is its new, standards-compliant rendering mode.
Previous IE versions had legacy problems with the inheritance of styles in block-level elements like tables. They didn't inherit. Most notably, previous versions did not propagate styles to td cells properly, so you needed to duplicate style information for these elements. If you did indeed want a td element centered you had to explicitly set the style and then test the style propagation thoughoughly as other elements could surprise you.