scholarly journals Some remarks about minimal prime ideals of skew Poincaré-Birkhoff-Witt extensions

2020 ◽  
Vol 30 (2) ◽  
pp. 207-229
Author(s):  
A. Niño ◽  
◽  
A. Reyes ◽  
Keyword(s):  
Prime Ideals ◽  
Noncommutative Rings ◽  
Polynomial Type ◽  
Ore Extensions ◽  
Skew Pbw Extensions ◽  
Minimal Prime

In this paper, we characterize the minimal prime ideals of skew PBW extensions over several classes of rings. We unify different results established in the literature for Ore extensions, and extend all of them to a several families of noncommutative rings of polynomial type which cannot be expressed as these extensions.

scholarly journals Minimal prime ideals of skew PBW extensions over 2-primal compatible rings

2020 ◽  
Vol 54 (1) ◽  
pp. 39-63
Author(s):  
Mohamed Louzari ◽  
Armando Reyes
Keyword(s):  
Commutative Rings ◽  
Prime Ideals ◽  
Noncommutative Rings ◽  
Polynomial Type ◽  
Ore Extensions ◽  
Skew Pbw Extensions ◽  
Minimal Prime

In this paper, we characterize the units of skew PBW extensions over compatible rings. With this aim, we recall the transfer of the property of being 2-primal for these extensions. As a consequence of our treatment, the results established here generalize those corresponding for commutative rings and Ore extensions of injective type. In this way, we present new results for several noncommutative rings of polynomial type not considered before in the literature.

scholarly journals A notion of compatibility for Armendariz and Baer properties over skew PBW extensions

2017 ◽  
pp. 157-178 ◽  
Author(s):  
Armando Reyes ◽  
Héctor Suárez
Keyword(s):  
Universal Enveloping Algebras ◽  
Noncommutative Rings ◽  
Enveloping Algebras ◽  
Ore Extensions ◽  
Skew Pbw Extensions

In this paper we are interested in studying the properties of Armendariz, Baer, quasi-Baer, p.p. and p.q.-Baer over skew PBW extensions. Using a notion of compatibility, we generalize several propositions established for Ore extensions and present new results for several noncommutative rings which can not be expressed as Ore extensions (universal enveloping algebras, diffusion algebras, and others).

A NOTE ON COMPLETELY PRIME IDEALS OF ORE EXTENSIONS

2010 ◽  
Vol 20 (03) ◽  
pp. 457-463 ◽  
Author(s):  
V. K. BHAT
Keyword(s):  
Prime Ideal ◽  
Prime Ideals ◽  
Recent Past ◽  
Associated Prime Ideals ◽  
Ore Extensions ◽  
Active Research ◽  
Considerable Work ◽  
Minimal Prime ◽  
Associated Prime ◽  
Completely Prime Ideal

The study of prime ideals has been an area of active research. In recent past a considerable work has been done in this direction. Associated prime ideals and minimal prime ideals of certain types of Ore extensions have been characterized. In this paper a relation between completely prime ideals of a ring R and those of R[x; σ, δ] has been given; σ is an automorphisms of R and δ is a σ-derivation of R. It has been proved that if P is a completely prime ideal of R such that σ(P) = P and δ(P) ⊆ P, then P[x; σ, δ] is a completely prime ideal of R[x; σ, δ]. It has also been proved that this type of relation does not hold for strongly prime ideals.

Skew Poincaré–Birkhoff–Witt extensions over weak compatible rings

2019 ◽  
Vol 19 (12) ◽  
pp. 2050225 ◽  
Author(s):  
Armando Reyes ◽  
Héctor Suárez
Keyword(s):  
Algebraic Geometry ◽  
Theoretical Physics ◽  
Quantum Algebras ◽  
Noncommutative Rings ◽  
Noncommutative Algebraic Geometry ◽  
Ore Extensions ◽  
Skew Pbw Extensions ◽  
Weak Notion

In this paper, we introduce weak [Formula: see text]-compatible rings and study skew Poincaré–Birkhoff–Witt extensions over these rings. We characterize the weak notion of compatibility for several noncommutative rings appearing in noncommutative algebraic geometry and some quantum algebras of theoretical physics. As a consequence of our treatment, we unify and extend results in the literature about Ore extensions and skew PBW extensions over compatible rings.

On minimal prime ideals of commutative Bezout rings

1999 ◽  
Vol 51 (7) ◽  
pp. 1129-1134
Author(s):  
B. V. Zabavskii ◽  
A. I. Gatalevich
Keyword(s):  
Prime Ideals ◽  
Minimal Prime

scholarly journals Characterizations of m-Normal Nearlattices in terms of Principal n-Ideals

2013 ◽  
Vol 38 ◽  
pp. 49-59
Author(s):  
MS Raihan
Keyword(s):  
Prime Ideal ◽  
Prime Ideals ◽  
Single Element ◽  
Finitely Generated ◽  
Fixed Element ◽  
Minimal Prime

A convex subnearlattice of a nearlattice S containing a fixed element n?S is called an n-ideal. The n-ideal generated by a single element is called a principal n-ideal. The set of finitely generated principal n-ideals is denoted by Pn(S), which is a nearlattice. A distributive nearlattice S with 0 is called m-normal if its every prime ideal contains at most m number of minimal prime ideals. In this paper, we include several characterizations of those Pn(S) which form m-normal nearlattices. We also show that Pn(S) is m-normal if and only if for any m+1 distinct minimal prime n-ideals Po,P1,…., Pm of S, Po ? … ? Pm = S. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16548 Rajshahi University J. of Sci. 38, 49-59 (2010)

scholarly journals Hopf algebras and skew PBW extensions

2019 ◽  
Vol 10 (2) ◽  
Author(s):  
Luis Alfonso Salcedo Plazas
Keyword(s):  
Hopf Algebra ◽  
Hopf Algebras ◽  
Ore Extensions ◽  
Skew Pbw Extensions

In this article we relate some Hopf algebra structures over Ore extensions and over skew PBW extensions ofa Hopf algebra. These relations are illustrated with examples. We also show that Hopf Ore extensions andgeneralized Hopf Ore extensions are Hopf skew PBW extensions.

Elements of Minimal Prime Ideals in General Rings

2010 ◽  
pp. 69-81 ◽  
Author(s):  
W. D. Burgess ◽  
A. Lashgari ◽  
A. Mojiri
Keyword(s):  
Prime Ideals ◽  
Minimal Prime

Semicritical Rings and the Quotient Problem

1984 ◽  
Vol 27 (2) ◽  
pp. 160-170
Author(s):  
Karl A. Kosler
Keyword(s):  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Prime Ideals ◽  
Regular Elements ◽  
The Right ◽  
Minimal Prime ◽  
Necessary And Sufficient ◽  
Quotient Rings ◽  
The Relationship

AbstractThe purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/Ki, i = 1,…,n, possess artinian classical quotient rings and regular elements in R/Ki lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.

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