## The new encyclopaedia Britannica: in 32 vol. Macropaedia, Accounting - Architecture, Volume 13 |

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Page 291

sion one — the coordinate

between geometry and arithmetic, which has been intensively generalized and

fruitfully ...

sion one — the coordinate

**ring**of H has many properties in common with the**rings**of algebraic integers studied by the arithmeticians, a striking parallelismbetween geometry and arithmetic, which has been intensively generalized and

fruitfully ...

Page 292

The

elements except 0. The fourth example involves polynomials and power series

with coefficients ak in R, a commutative unitary

sums ...

The

**rings**in the first two examples (308 and 309), however, have no nilpotentelements except 0. The fourth example involves polynomials and power series

with coefficients ak in R, a commutative unitary

**ring**. A letter X and formal finitesums ...

Page 294

The

except itself and 0. It may be viewed as an algebra over K, with ri1 basis

elements, namely, the matrices Epq{ 1 < p, q < «), in which Em has a 1 at the

intersection of ...

The

**ring**of n X n matrices over K is denoted by M„(K). It has no two-sided idealexcept itself and 0. It may be viewed as an algebra over K, with ri1 basis

elements, namely, the matrices Epq{ 1 < p, q < «), in which Em has a 1 at the

intersection of ...

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