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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.
For sale - FLIR PTS536 thermal weapon sight. Incorporates a 12 micron Boson detector and 4x optical zoom for a very nice crisp image. QD return to zero picatinny mounting and multiple weapon profiles, and in excellent condition.
With case. $2800 shipped conus
Minty S&W M&P 15 II with 1/9 melonited Government profile barrel. Mint condition. $750 firm for now; few trade interests below.
Pretty much as new except:
a) Added a 1x green dot fiber optic. Is NOT a trijicon, just looks like one, a "fakog." Nice small green dot, co-witnessed. Fun.
b)...
Hello All,
I have a Yugo M70 (I believe it its a M70AB1 but I'm not 100% sure) for sale with 2 metal 30rd magsfor sale. It's an excellent 1977-79 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...
Selling my Ruger GP100 357 Magnum, it's the stainless model with a 4.2" barrel, 6 shot, DA/SA, adjustable rear sight. Super smooth action, great DA shooting gun. I have upgraded the stock grip to a Pachmayr Diamond Pro rubberized grip, big improvement over the stock Hogue in my opinion. I...
Western Field shotgun.
Made by Mossberg. Model 550AB 12ga, 2 1/2 and 3" shells, 30" fixed Full Choke barrel with bead.
Serial number D62XXX. From internet files, this indicates a build date prior to 1973.
The shotgun is in excellent condition. Only a few very small marks in the walnut stocks...
M1 Garand For Sale.
This is a 1945 Springfield Armory M1 rifle in 30-06. Standard size. Condition is excellent.
Most of the parts are age correct, some are newer.
It is an Arlington Ordnance import, returned from South Korea Forces after a rebuild, and an Arlington Ordnance barrel (Citadel 4...
This is in excellent condition with approximately 200 rounds through it.
Rosewood grips.
3” barrel.
Aluminum frame.
Satin stainless slide.
Full meltdown treatment.
One Kimber 6 round mag.
One Wilson Combat 7 round mag.
Not interested in trades at all.
Cash only.
Best way to contact is...
PLEASE READ
For sale I have a Taurus 856 6-shot revolver chambered for .38 Special as well as an ammo can with 400+ loose rounds. I'm asking $350 for everything but I would be willing to trade the ammo for the following calibers and bring the price of the gun down to $200.
7.62x39
7.62x38R...
I have a Magpul Tripod Sling Stud QD (Black) in excellent condition and perfectly functional. I am asking $60 cash for it, which is about 1/2 price of a new unit. I am in Seattle and could meet in Queen Anne or South Lake Union. I can also ship the unit for extra $6 (USPS First Class Mail), but...
Remington 700 .223 varmit laminated stock with a 26” bull barrel. Excellent condition, little ding under the grip but no major marks. Non threaded. Knock off haris bipod. This gun is in excellent condition. Shoots 1/2” moa with light grain bullets.
$800 local sell only FTF at A cut Above pawn...
I have a 1965 Ithaca model 37 feather light 20 gauge with an ammo can full of shells. Buck shot and bird shot. This shotgun is in excellent condition, this model will slamfire.
I will sell for $500 cash only.
No trades, local sell only.
Transfer at A cut Above.
Thanks for looking
SOLD SOLD SOLD
Beretta 92FS
Many will call this the most reliable gun ever made ! I couldn't argue that point as the US military, NATO forces, our own secret service and freedom fighters around the world have been relying on it for over four decades of service. That's hard to beat !!!
I have...
I was looking for a rifle with a little more horsepower than my son’s 6.5 Grendel that he is shooting now. So I picked up a couple of nice 260 Remington rifles over the last couple months. This one and a Kimber Montana. We haven’t shot either one yet, but he said that he prefers the Montana...
Hello there,
I'm moving across the country soon and want to sell off a few "nonessential" firearms. I bought this Maverick 88 new from NW Armory 2 years ago and have only put about 25 rounds through it. That was in one sitting; it was cleaned, and hasn't really been touched since. It's got a...
$850
Wilson Combat M2 2 stage trigger
Magpul forend and stock
Wilson Combat grip and Flash hider
Approximately 150 rounds through it
No trades at this time
PRICE FIRM