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In commutative algebra, a quasi-excellent ring is a Noetherian commutative ring that behaves well with respect to the operation of completion, and is called an excellent ring if it is also universally catenary. Excellent rings are one answer to the problem of finding a natural class of "well-behaved" rings containing most of the rings that occur in number theory and algebraic geometry. At one time it seemed that the class of Noetherian rings might be an answer to this problem, but Masayoshi Nagata and others found several strange counterexamples showing that in general Noetherian rings need not be well-behaved: for example, a normal Noetherian local ring need not be analytically normal.
The class of excellent rings was defined by Alexander Grothendieck (1965) as a candidate for such a class of well-behaved rings. Quasi-excellent rings are conjectured to be the base rings for which the problem of resolution of singularities can be solved; Heisuke Hironaka (1964) showed this in characteristic 0, but the positive characteristic case is (as of 2016) still a major open problem. Essentially all Noetherian rings that occur naturally in algebraic geometry or number theory are excellent; in fact it is quite hard to construct examples of Noetherian rings that are not excellent.
Excellent condition, minimal rounds through…maybe 100. I just don’t shoot much.
All components were new when I assembled this.
-Spikes “Punisher” lower
-PSA complete upper, 10.5” nitrided barrel
-LAW folder with Thorsden brace mounted
-PrimaryArms MD-ADS red dot, mounted on quality ADM mount...
Sako 94 S $2000.00 + shipping
Lilja Match Barrel
Jewell Trigger 2 oz +
Original Box , Stock and Barrel Excellent
Burris 6x Mini Scope and Box
Bank Certified Check or United States Postal Money Order
In excellent shape with only minimal signs of usage. Ran about 75 rounds through the rifle, then changed to a different Geiselle trigger. Rather than let this great trigger sit in the drawer, it is time for someone to put it to use. Save some money and buy this now for $140! As pricing is an art...
Up for sale or trade is a beautiful original 3 band 1863 Model Springfield Rifle. This .58 cal rifle was the standard infantry issued firearm for the Union Army during the Civil War and remained in service for some time after. This rifle is in excellent condition. The bore is bright and rifling...
Springfield Armory XD Tactical, 5" w/ 1-16rnd factory magazine.
Face to face in Medford, Grants Pass and surrounding areas. No shipping.
Willing to meet half way at agreed upon dealer.
I purchased used and in great condition. Have not fired but gun cycles fine.
Looking to sell quick to fund a...
Up for sale is my Ruger Charger .22 cal. In excellent condition. Less than 500 rounds fired since purchased new in 2019.
Only things added to the pistol are an after market bolt buffer pin and a flash hider. I will include the stock pin and thread cap as well as a soft case. Also comes with...
SOLD PENDING TRANSFER 11/16/22
For sale is an excellent condition Remington 870 Tactical 12 gauge shoots 3" shells and less. I've owned it for almost 15 years. I bought it new and have shot it a few times and kept it clean and lubed and stored in a climate controlled safe.
Nice and all...
Today shot a old Swedish Excellent Gevaret C11 K .177 roundball multi-pump.
There were several models made. some with smooth bore and rifling in the last few inches of the barrel others are fully rifled. They offered both full size and carbine. The K signified carbine . They where available...
Original owner with ~1.5k fired.
Pistol is in excellent condition with no dings, nicks, scratches, abnormal wear or blemishes.
-Three 13 round magazines (Oregon sale only)
- Tru Dot night sights added
This is an excellent gun! Selling because I’m diving further down the double stack 1911 rabbit hole. Gun is in great condition and I’ve never had one malfunction with it! Holster is also in great condition and perfect for range use or outdoor carry. A great set up! Walk away with everything you...
I have, to the best of my knowledge, a preban, unfired hk91. It's in excellent condition, the real deal. Has telescoping stock, and also the psg1 adjustable stock, swivel bipod, 25 mags, and original and unfired 22 conversion kit, in factory box. The 25 mags also that come with it, are...
Up for consideration is great looking 1966 Red Seal $100 United States Note. While this is not a “Federal Reserve” note, it remains full legal tender. It also marks the first year of the $100 denomination since the conversion away from large bills in 1928. While I’m no grading expert, I do...