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A great gift for both parents and children, personalized name puzzles can be fun for the entire family. As a baby keepsake, parents can put it together and display it on a bookshelf in their baby ...
The following equivalent definitions of a left perfect ring R are found in Anderson and Fuller: [2]. Every left R-module has a projective cover.; R/J(R) is semisimple and J(R) is left T-nilpotent (that is, for every infinite sequence of elements of J(R) there is an n such that the product of first n terms are zero), where J(R) is the Jacobson radical of R.
Gilbert cloud chamber, assembled An alternative view of kit contents. The lab contained a cloud chamber allowing the viewer to watch alpha particles traveling at 12,000 miles per second (19,000,000 m/s), a spinthariscope showing the results of radioactive disintegration on a fluorescent screen, and an electroscope measuring the radioactivity of different substances in the set.
Let C be an additive category, or more generally an additive R-linear category for a commutative ring R. We call C a Krull–Schmidt category provided that every object decomposes into a finite direct sum of objects having local endomorphism rings. Equivalently, C has split idempotents and the endomorphism ring of every object is semiperfect.
A secret decoder ring (or secret decoder) is a device that allows one to decode a simple substitution cipher—or to encrypt a message by working in the opposite direction. [ 1 ] As inexpensive toys, secret decoders have often been used as promotional items by retailers, as well as radio and television programs, from the 1930s through to the ...
The classical ring of quotients for any commutative Noetherian ring is a semilocal ring. The endomorphism ring of an Artinian module is a semilocal ring. Semi-local rings occur for example in algebraic geometry when a (commutative) ring R is localized with respect to the multiplicatively closed subset S = ∩ (R \ p i ) , where the p i are ...