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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.
-One owner in excellent condition with ~ 500 rounds fired
This is the Gen. 3 SF (short frame) version; Glock introduced this with a reduced grip circumference making it more manageable for folks with smaller hands.
-100% stock, box and factory accoutrements included
-2 ea. 13 round magazines (...
Stored under cover since day one. Original owner. 2006 Comfort 26' total length 5,300 lbs approximately.
NEW tires, brakes and bearings. Full clean after every use. Still smells new. $8,000
Thank you
SOLD. For sale is a Gen 3 Glock 23 in excellent condition. Round count is approximately 500 to 600. I've owned this since it was new.
WA residents: Price is $400 and it will include one 10rd magazine.
ID residents and where legal: Price is $450 and it will include one 10rd and six 13rd...
***SOLD***For sale is a Sig P229R .40 S&W in excellent condition. Can be easily converted to .357 Sig with barrel only (not included). Round count is approximately 600. I believe I bought this one back in about 2008.
WA residents: Price is $500, but unfortunately I cannot include the mags since...
Selling an original Monson, MA Dan Wesson 744 VH. Educated guesses say it was manufactured in 1983. Gun shoots like a dream. Mirror bright bore, Cylinder locks up tight. Selling because I just want something with a bit more after market support. Comes with original wood grip, an additional...
This is a very lightly used CZ 75bd with decocker. 9mm, 4.7 barrel, 2 16 rd. magazines,
$500, or will trade for nice hunting rifle, prefer savage, but open.
Photos are current 100% authentic. No scratches or wear, well maintained. Only light target loads fired. 4” Barrel, Blackhawk Holster included. Gunbroker has these selling at $1149 used. No trades
Benchmade 940-1 Osborne Carbon Fiber, Lifetime Warranty, reverse tango blade, mini deep carry pocket clip, extremely light, it comes with Benchmade’s free sharpening for life (just like all Benchmade’s)….
The only reason I’m selling it is to thin my collection.
I will not respond to “is...
Benchmade 940-1 Osborne Carbon Fiber, Lifetime Warranty, reverse tango blade, mini deep carry pocket clip, extremely light, it comes with Benchmade’s free sharpening for life (just like all Benchmade’s)….
The only reason I’m selling it is to thin my collection.
I will not respond to “is...
Excellent condition 1974 vintage Colt Trooper MKIII 357 Magnum with nickel finish and 4" barrel.
Collectable solid shooter at half the price of a Python.
Solid lock-up and timing with clear shiny bore.
I am willing to ship to your FFL, buyer pays shipping.
For local sale, I will transfer at my...
This is in excellent condition with drawers liners in all drawers with minimal wear to liners.
Top and bottom lock and keys are present.
Locking wheels.
Bottom is Red, 8 drawer.
26.75” w x 18” d x 40.25” tall from ground.
Top is Red, 10 drawer.
26” w 16” d 19.5” h
Serious inquiries only and...
Up for grabs is a solid vintage spotting scope from tasco, model 3701 in camo. Includes the tripod, handle and factory covers for each end. This one has no issues, clear glass and has always been stored indoors. It’s as close to new as you’re going to get on one this old. Great scope!
Asking...
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...