rschwieb
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98/100 score
 Apr 28 comment Let R* be the set of units of R and S* be the set of units of S. Prove that f(R*) = S*. @s.harp well, ring isomorphisms of rings with identity preserve identity whether or not that is among your axioms :) Apr 28 revised Commutativity of a ring from idempotents. added 117 characters in body Apr 28 comment Sum of nil right ideals @karparvar there are obviously elements of arbitrarily high index of nilpotency. Apr 28 comment Sum of nil right ideals @karparvar there are obviously elements of arbitrarily high index of nilpotency. Apr 28 answered Commutativity of a ring from idempotents. Apr 27 comment Rings in which $ab=0$ implies $axb=0$ @Gro-Tsen well, not many people have these definitions in their heads at all times. This is a great example of a bunch of closely knit conditions that "tease apart" particular aspects of something that happens in a commutative ring. (The nilpotent elements forming an ideal) it's also nice to see the variety of examples it produces Apr 27 comment Rings in which $ab=0$ implies $axb=0$ @Gro-Tsen I'm glad you like it! I really need to get back to work on that website. Apr 27 comment Direct Summands of PI Rings as Right Ideals @karparvar I don't know. It rarely comes up in this context for me Apr 27 answered Rings in which $ab=0$ implies $axb=0$ Apr 27 answered Direct Summands of PI Rings as Right Ideals Apr 27 comment Is there an adjective for rings whose every non-zero prime ideal is maximal? @goblin No mind reading is necessary when the topic appears in every commutative algebra text and all over the web. Perhaps 'tone' is the wrong word to describe this unnecessary tax on my comment writing. Anyhow, I'm sure you will consult the literature first in the future. Regards Apr 27 revised Is there an adjective for rings whose every non-zero prime ideal is maximal? added 66 characters in body Apr 27 comment Is there an adjective for rings whose every non-zero prime ideal is maximal? @Crostul nearly exact: that omits fields, which vacuously satisfy the condition Apr 27 comment Is there an adjective for rings whose every non-zero prime ideal is maximal? @goblin No, I am not going to explain how to read the definition of Krull dimension to you, since I know you are perfectly capable of reading it on the wiki. These imprecisions you see are the result of working on a mobile phone. Perhaps you can take this into consideration next time before writing responses with such tones. Regards Apr 27 answered Is there an adjective for rings whose every non-zero prime ideal is maximal? Apr 27 comment Is there an adjective for rings whose every non-zero prime ideal is maximal? @goblin the krull dimension of a ring is the supremum of such chains, so such a ring would not even have finite krull dimension, much less dimension 1 or 0 Apr 27 comment Is there an adjective for rings whose every non-zero prime ideal is maximal? @goblin krull dimension counts the "links" between elements of the chain rather than the elements in the chain, so no, the integers are one dimensional. Apr 26 awarded Nice Question Apr 22 comment are Orthogonal vectors superior to independent non Orthogonal ones? @Travis OK, thanks for answering. Apr 22 comment are Orthogonal vectors superior to independent non Orthogonal ones? @Travis Just curious: what sense of 'natural' are you thinking of?