نتایج جستجو برای: weakly noetherian

تعداد نتایج: 44697  

2002
T. Gateva-Ivanova Eric Jespers Jan Okniński

We consider algebras over a field K defined by a presentation K〈x1, . . . , xn : R〉, where R consists of ( n 2 ) square-free relations of the form xixj = xkxl with every monomial xixj , i 6= j, appearing in one of the relations. Certain sufficient conditions for the algebra to be noetherian and PI are determined. For this, we prove more generally that right noetherian algebras of finite Gelfand...

2007
Silvio Ghilardi Enrica Nicolini Silvio Ranise Daniele Zucchelli

In abstract algebra, a structure is said to be Noetherian if it does not admit infinite strictly ascending chains of congruences. In this paper, we adapt this notion to first-order logic by defining the class of Noetherian theories. Examples of theories in this class are Linear Arithmetics without ordering and the empty theory containing only a unary function symbol. Interestingly, it is possib...

2005
HANS SCHOUTENS

Let R be a Noetherian local ring and Ω an arbitrary R-module of finite depth and finite projective dimension. The flat dimension of Ω is at least depth(R)−depth(Ω) with equality in the following cases: (i) Ω is finitely generated over some Noetherian local R-algebra S; (ii) dim(R) = 1; (iii) dim(R) = 2 and Ω is separated; (iv) R is CohenMacaulay, dim(R) = 3 and Ω is complete.

1970
DAVID EISENBUD

An easy consequence of this is that a left Noetherian (respectively left Artinian) ring which is finitely generated over its center is right Noetherian (respectively right Artinian). Theorem 1 follows easily from Theorem 2, which gives a partial converse to the following standard fact: IfR C S are rings, and ifQ is an injective R-module, then Hom~(S, Q) is an injective S-module (this follows, f...

2006
Abderezak OULD HOUCINE

We collect in this paper some remarks and observations about limit groups of equationally noetherian groups. We show in particular, that some known properties of limit groups of a free group or, more generally, of a torsion-free hyperbolic group can be seen as consequences of the fact that such groups are equationally noetherian. Especially, such properties are still true for linear groups and ...

2007
Sophie Frisch

Skolem and Nullstellensatz properties are analogues of the weak Nullstellensatz and Hilbert’s Nullstellensatz, respectively, for the ring of integervalued polynomials in several indeterminates Int(D) = {f ∈ K[x1, . . . , xn] | f(D) ⊆ D}, where D is a domain and K its quotient field. We show their equivalence when D is a Noetherian domain and extend the criterion of Brizolis and Chabert for Int(...

2005
BRIAN CONRAD

Suppose X is a locally noetherian Deligne–Mumford stack. Definition 1.2 has an obvious variant X̂ét using the underlying smaller étale site Xét and the restriction Oc Xét of Oc X to this site. By [3, 12.7.4], the category of cartesian Oc X -modules on Xlis-ét is equivalent to the category of Oc Xét-modules on Xét: (1.1) ModXlis-ét,cart(Oc X ) ' ModXét(Oc Xét) Definition 1.3. Let X be a locally n...

2015
YIFEI ZHAO

We organize this set of notes around a few theorems of Weierstrass. Write OCn for the sheaf of holomorphic functions on C. In the first three sections, we deduce the following “algebraic” results as consequences of the Weierstrass theorems: (i) for each open set Ω ⊂ C, the ring OCn(Ω) is not Noetherian, (ii) the local ring OCn,0 is factorial, (iii) the local ring OCn,0 is Noetherian. The two la...

1996
S. DǍSCǍLESCU L. VAN WYK

We first provide an example of a ring R such that all possible 2 × 2 structural matrix rings over R are isomorphic. However, we prove that the underlying graphs of any two isomorphic structural matrix rings over a semiprime Noetherian ring are isomorphic, i.e. the underlying Boolean matrix B of a structural matrix ring M(B,R) over a semiprime Noetherian ring R can be recovered, contrary to the ...

2014
B. Satyanarayana L. Krishna R. Durga Prasad

The notion of intuitionistic fuzzy positive implicative hyper BCK-ideals of type-1, 2... 8 of hyper BCK-algebras was introduced in 2012 by Durga Prasad, Satyanarayana and Ramesh. In this paper, we investigate some related properties of intuitionistic fuzzy positive implicative hyper BCK-ideals of types-1. We characterize positive implicative Artinian (shortly, PI-Artinian) hyper BCK-algebras of...

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