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The center of a simple ring is necessarily a field. It follows that a simple ring is an associative algebra over this field. It is then called a simple algebra over this field. Several references (e.g., Lang (2002) or Bourbaki (2012)) require in addition that a simple ring be left or right Artinian (or equivalently semi-simple).
Ruby ring. A ring is a round band, usually made of metal, worn as ornamental jewelry.The term "ring" by itself denotes jewellery worn on the finger; when worn as an ornament elsewhere, the body part is specified within the term, e.g., earrings, neck rings, arm rings, and toe rings.
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1990s bling and multiple rings are some of the biggest 2025 jewelry trends. Justin Lambert/Getty Images. ... the stylist recommends looking for simple, high-quality pieces that will last forever. ...
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By the Artin–Wedderburn theorem, a central simple algebra is the matrix ring of a division ring; thus, each similarity class is represented by a unique division ring. For example, Br( k ) is trivial if k is a finite field or an algebraically closed field (more generally quasi-algebraically closed field ; cf. Tsen's theorem ).
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Every simple ring R with unity is both left and right primitive. (However, a simple non-unital ring may not be primitive.) This follows from the fact that R has a maximal left ideal M, and the fact that the quotient module R/M is a simple left R-module, and that its annihilator is a proper two-sided ideal in R.