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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.
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
$450.00 +...
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...
White's Insulated Hunter Boots in excellent condition
Mens Size 11 1/2
Wide E
Hand made in Spokane WA USA
Reference:
https://shop.whitesboots.com/all-boots/insulated-hunter/
Very little use. Prefer local sale.
I am selling this upgraded Mark IV Ruger with the carrying case and two 10rd magazines. This Ruger was upgraded for competition with the following mods and it is being sold because it is not being used.
LIST OF UPGRADES
Volquartsen Accurizing Kit, original cost $111.00
Volquartsen Bolt Tuneup...
Please send trade offers and comments thru the contact PM messenger...Thanks
Leupold Mark 8 Rifle Scope 3.5-25 x 56
Leupold Mk 8
Part# 171845
Mil
3.5-25x56 Long Range Scope
ZeroLock
Tremor 3 Reticle
**Lightly Used In Excellent Condition**
$2200 Cash (firm on cash price)
Partial/ Full Trade...
Please Note: $140 for Bare Bow or $220 for Setup as shown in the Photo's
Sold Pending Funds
70lb L.H. Bear Encounter Compound Bow
All set up and ready to shoot
It is set at 29" draw but the module can be re-positioned for longer or shorter draw
Comes as you see in the photo and includes a...
Nice clean Harris Bipod that came with a used rifle that I bought. Needs a new home. Bipod in pics is the exact one that you will receive. Cross posted so First I'll take it followed by an IM or email gets the goods. Several payment options available. Thanks for looking!
I have both a full-sized and compact SAR K2's .45ACP in STAINLESS; excellent condition! Both have key upgrades: Galloway Precision spring kit installed (original springs included) which makes this a very, very good DA/SA trigger. Also, extra grip panels by Tillander...the original grip panels...
Kimber Micro 380 - Excellent Condition - $475
Less than 500 rounds. 3, 7 round magazines. DeSantis Gun Hide holster. Case and box. Shoots great, just need funds for next purchase.
**SPF to Buster Beaver** I have an absolutely beautiful HK91 with IB (1981) date code available for sale. This rifle has seen very little use and is in excellent almost as-new condition overall. There are some signs of use but very little although it does look like it may have had a claw mount...
Hi, up for sale is a bomb 💣 resistant shorty AR. This setup is new/unfired with the exception of the barrel, which is a take off from a Springfield Saint pistol. It has a tucked in Noveske Flaming Pig + one of the coolest DPMS sight setups I've ever come across, super tough💪. Head space and BCG...
Hello! I have an SKS Norinco for sale in excellent condition. I am selling it because I would like to make some room in my collection and just go with 5.56 only and selling my 7.62x39 items. I have never fired this SKS. I purchased it from a collector who was selling it from their...
Please PM your Questions and Comments ... Thank you
Note: If you transfer at HighLine in Newberg then I will pay the transfer fee
Bergara B-14 HMR 6.5 Creedmore Rifle w/22" Threaded Barrel for sale
Includes:
Original Box and Paper work
20 MOA Picatinny Scope Base
Less then 200 rounds fired...
Sig RomeoZero Micro Open Reflex Sight, Black
Came with my 365xl, in perfect shape and will come with a brand new sealed battery. All original instructions / hardware is included.
Kept clean and sealed in bag once taken off the slide.
$120.00 $100
Cash, no trades
No delivery / shipping
Pickup /...
Hello All,
I have a Yugo M70 (I believe it its a M70B1) for sale with 2 metal 30rd mags for sale. It's an excellent Yugo Surplus parts build on a US receiver. Cool ex-comblock military AK. It's an excellent shooter. The furniture currently on it is a placeholder as I planned on picking up a new...
For sale is a 1980 Marlin 39A. Like all Marlin 39As this one is a tack driver. See 75 yrd. 3 shot group below shot with a receiver sight
I'd say the blueing is about 95+ % No rub marks except a little at the muzzle and some light scratches on the mag tube
The wood has no deep scratches or...
Up for Sale is a Walther P99 AS. Took it to the range once, less than 60 rounds through the pipe. Cleaned and oiled right after range visit. Arguably, coming with one of the most innovative and shortest reset stock triggers ever on a polymer frame.
"Legacy and innovation collide to create one...