Computation of point modules of finitely semi-graded rings

Abstract

In this paper we compute the set of point modules of finitely semi-graded rings. In particular, from the parametrization of the point modules for the quantum affine n-space, the set of point modules for some important examples of non N-graded quantum algebras is computed.

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

“…Last, but not least, we consider as a possible future work to investigate minimal prime ideals and the 2-primal property in a more general context of noncommutative rings than skew PBW extensions such as for example the semi-graded rings introduced by Lezama [33] (see also [29] and [32]), or maybe considering a weak notion of compatibility following the ideas presented recently by the second author [57], and of course, in the setting of modules over these extensions, see [36], [42], and [48].…”

“…Some words about the generality of skew PBW extensions with respect to another families of noncommutative rings are said in Section 1. Homological and ring-theoretical properties for these extensions have been investigated by several people (e.g., Artamonov [2], Hashemi et al, [17], [18], [19], and [20], Lezama et al, [1], [24], [29], [31], [33], [35], Louzari et al, [37], Tumwesigye et al, [61], Zambrano [62], and the authors, [42], [43], [48], [51], [52] and [55]). As a matter of fact, a book containing research results about these extensions has recently been published, see [10].…”

Skew PBW extensions over symmetric rings

“…Ore extensions of injective type are strictly contained in skew PBW extensions (this is not possible for original PBW extensions; see [32], for a list of noncommutative rings which are skew PBW extensions but not iterated Ore extensions). Several ring and module theoretical properties of skew PBW extensions have been established by different people (e.g., Acosta [1], Artamonov [4], Hamidizadeh et al [15], Hashemi et al [17], [18], [19], Lezama et al [14], [22], [27], [28], [29], [30], [31], [32], [33], Louzari [35], Niño et al [39], [40], Tumwesigye et al [54], Zambrano [55], and the authors [49], [50], [52], [53]). A book containing research results about these extensions has recently been published (see Fajardo et al [11]).…”

$Σ$-semicommutative rings and their skew PBW extensions

“…Regarding the objects of interest in this article, the skew PBW extensions, these objects were defined by Gallego and Lezama [17] with the aim of generalizing families of noncommutative rings as PBW extensions introduced by Bell and Goodearl [8], skew polynomial rings (of injective type) defined by Ore [42], and other as solvable polynomial rings, diffusion algebras, some types of Auslander-Gorenstein rings, some Calabi-Yau and skew Calabi-Yau algebras, some Artin-Schelter regular algebras, some Koszul algebras (see [16] or [46] for a detailed reference to each of these families). Several ring and theoretical properties of skew PBW extensions have been investigated by some people (e.g., Artamonov [5], Fajardo et al [16], Hamidizadeh et al [21], Hashemi et al [22], Lezama [34], and Louzari et al [38]). Precisely, the authors have studied the ring-theoretical notions mentioned above in the setting of skew PBW extensions.…”