REFERRING to the review of Hilbert's “Grundlagen der Geometric,” on p. 394 of No. 2066 of NATURE (June 3), may I point out that the commutative law of addition can be proved without the help of any ...

NEITHER Dr. Hilbert nor the reviewer make any suggestion that the commutative law of addition is best proved as a deduction from the laws of multiplication. But the laws of multiplication are so often ...

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This is a preview. Log in through your library . Abstract Let $k$ be a commutative ring (with 1). We work with $k$-algebras with a grading mod 2, and with graded ...

This is a preview. Log in through your library . Abstract For any finite commutative multiplicative monoid S with an element 0 such that S0 = {0} ≠ S, some decompositions of S are given as the ...