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excellent
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.
Ultimate range Staccato very fast shooting and super accurate. Gunsmith installed trigger and all receipts available. Have $5117.00 invested. Super clean excellent condition. Staccato quality and accessories at very low price.
Great Kayaks, Old Town- Trip 10 Angler DLX, Perception Prodigy 100 with 2 adjustable paddles, Lifetime kayak carrier, 2 whistles and pump, special console for storage.
2 brand new never worn Onyx life jackets, medium and large. I can send specific pictures if you need!
Always kept in garage...
Up for sale a beautiful vintage generator. A true survivor with very little use. Only clear gas has been used across its life in an effort to mitigate gumming the carb. It's initial use case was as a power backup on a store register, so was only fired up to keep it working. After that, it's only...
Benelli M4 LE version, 7 round tube, 5 position stock. Ghost Ring Night Sights, No modifications, and outstanding condition.
Has the new style forearm that shrouds the barrel and permits mounting lights up front. All paperwork, manual, forward rails, and the oil that came with the gun is...
I bought this new. I've had surgery on one thumb and will have another next year. It's turned into a paperweight for me. My 70 year old hands will never be able to rack it I'm afraid. I've put approximately 300-400 rounds through it without any glitch at all. Always meticulously cleaned after...
Found one of my grail guns and need to offload some stuff to foot the bill... have a like new glock 20 gen 4 as the title states. Pistol is in all but perfect condition and comes with factory box, papers,etc. (2) 15 round glock factory mags, (1) 15 round mag with a +2 extension, (2) boxes...
Black finish with brown handgrip, minimally used. With carrying case, trigger lock, and HKS fast reload. $999. I have been the only owner of this pistol. Sale will take place in SafeFire Indoor shooting Range and Retail, 4857 NW Lake Road # 210, Camas, Wa 98607. I live in Camas.
Here's a great opportunity to own a Used but Excellent Condition Ruger Red Label Shotgun. We have 2 for Sale. One is a 30" and the other is a 26" Over & Under 12 Gauge. These two are in stock and ready for a new home.
1. Ruger Red Label 30" 12 Gauge: $1799...
Bought this Ruger LCR in 22lr a year ago because I thought it’d be an easy pistol for my grandparents-in-law to shoot. Turns out, they’re not necessarily gun-friendly folks. So, I have no need for this and would like to fund a different purchase.
Bought it from guns.com in excellent condition...
The gun is the stainless steel frame version and is in EXCELLENT condition. I want to emphasize how pristine this gun is. It will be extremely difficult to find a better-conditioned gun like this one. The asking price is $1000 cash only, no trades.
## I WILL LET IT GO FOR $750 for this week...
Savage Model 11 .308 Synthetic Stock. Leupold Scope ( I can sell with or without scope). $450 or best offer. 22" barrel. Sling. I never hunted with this rifle. I fired one box of rounds and sighted it in., Very nice and very inexpensive way to get into hunting. Jan Kitchel 503-730-0685
CZ Scorpion EVO 3 S1 in Excellent Condition. Maybe 250 rounds through it and cleaned thoroughly. Comes with 7 mags and a bunch of spare parts (trigger, grip, thread protecter, etc.)
$550 must meet at a Portland Metro FFL that we agree on, buyer pays transfer fees. NO WA residents.
503-887-7600
Used, but never hunted with less than 200 shots, a true safe queen!
* Comes with Leupold bases and 30mm high Leupold rings
* RCBS reloading dies #13701
* Brass - 6 wby & 23 Federal Premium
* 1 – Lock-N-Load Modified Case 7mm wby
* 13 – Weatherby 160gr Accubond cartridges
* 17 - Federal Premium...
Duty carried magazines, in absolutely excellent condition, original Sig product made in Italy.
Would prefer selling all 8 together at $190, or $25 each if sold separately.
Putting this one up as it doesn't make it out of the safe enough. It is almost mint condition (see small pitting around rear sight). Serial dates it as 1968 Harrington and Richardson 949. It's the 9shoy SA/DA 22lr. It shoots flawlessly and most importantly, affordably. Bluing is in great...
An Excellent minty 1955 receiver dated Springfield Armory M1 Garand in 30.06. CMP expert grade. This garand is like brand new, does feature a brand new CBI (dated 01/22) barrel with a 0+ muzzle and throat rating. Also a brand new CMP walnut stock. Bolt is SA marked, oprod is HRA marked for...
Ruger SP101 .357 Mag excellent condition only a couple hundred rounds through it. Looking to trade for a sig p320 or p365 + - cash depending on the offer. Will also consider other 9mm semi autos.
Model Number: 5771
Caliber: 357 Mag
Front Sight Fiber Optic
Barrel Length 4.20"
Buyer pays...
I bought this from a member on this forum several years ago and have put less than 40 rounds through it. The majority being on the target in the picture. At some point a previous owner carved their initials in the stock, so I sanded it out and stained the rifle. I am not much of a shooter, but...
I have four 17-round CZ-75 magazines 9mm (but they work on any other cz-75 patterned pistols) made by Mec-Gar. Out of the package but either never used or have had a couple mags worth run through it so basically new. These go for $33-35 online plus shipping. $100 takes all 4 of them. Meet in or...
Black And Decker 5014 Rotary Hammer is in EXCELLENT CONDITION!
Not sure if it has been used. Looks NEW!
3/16 to 3/4 bit size.
Tested and works!
Carrying case, instruction, and paperwork included!
$150 Or Best Offer.