Skew Poincaré–Birkhoff–Witt extensions over weak zip rings

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

“…With this in mind, we consider the family of injective endomorphisms Σ and the family ∆ of Σ-derivations in a skew PBW extension A over a ring R established in Proposition 1. Examples and some ring theoretical properties of Σ-rigid rings have been established by the authors, see [43], [50], [55], [56] and [58].…”

“…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].…”

“…In Sections 2 and 3 we explicitly write the results we are extending. In [34], [55], and [58] there are several examples of these extensiones where the theory developed in both sections can be illustrated. In the last section, Section 4, we say a few words about the topic of interest in this paper and a possible future work.…”

A Classification of Ring Elements in Skew PBW Extensions Over Compatible Rings

“…B is reduced (note that there exists an endomorphism of a reduced ring which is not a rigid endomorphism, see [28], Example 9). Σ-rigid rings have been investigated in several papers (e.g., [47], [50], [58] and [59]).…”

“…Remark 3.11. The notion of compatibility has been very useful in the study of different ring theoretical properties of skew PBW extensions, for example see [51], [52], [59] and [60].…”