Algebra

\(\newcommand \ensuremath [1]{#1}\) \(\newcommand \footnote [2][]{\text {( Footnote #1 )}}\) \(\newcommand \footnotemark [1][]{\text {( Footnote #1 )}}\) \(\newcommand {\LWRframebox }[2][]{\fbox {#2}} \newcommand {\framebox }[1][]{\LWRframebox } \) \(\newcommand {\setlength }[2]{}\) \(\newcommand {\addtolength }[2]{}\) \(\newcommand {\setcounter }[2]{}\) \(\newcommand {\addtocounter }[2]{}\) \(\newcommand {\cline }[1]{}\) \(\newcommand {\directlua }[1]{\text {(directlua)}}\) \(\newcommand {\luatexdirectlua }[1]{\text {(directlua)}}\) \(\newcommand {\intertext }[1]{\\ \text {#1}\notag \\}\) \(\newcommand {\P } {\mathbb {P}}\) \(\newcommand {\R } {\mathbb {R}}\) \(\newcommand {\Z } {\mathbb {Z}}\) \(\newcommand {\N } {\mathbb {N}}\) \(\newcommand {\C } {\mathbb {C}}\) \(\newcommand {\Q } {\mathbb {Q}}\) \(\newcommand {\nwd }{\operatorname {NWD}}\) \(\newcommand {\nww }{\operatorname {NWW}}\) \(\let \str \longrightarrow \) \(\let \f \frac \) \(\let \vn \varnothing \) \(\let \s \subseteq \)