A signature-based algorithm for computing Gröbner-Shirshov bases in skew solvable polynomial rings by Zhao Xiangui, Zhang Yang

“…Signature-based algorithms are efficient algorithms for computing Gröbner-Shirshov bases in commutative polynomial rings, and some noncommutative rings. In this paper, we first define skew solvable polynomial rings, which are generalizations of solvable polynomial algebras and (skew) PBW extensions. …”
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Homogenized skew PBW extensions by Héctor Suárez, Armando Reyes, Yésica Suárez

“…Abstract In this paper, we provide a new and more general filtration to the family of noncommutative rings known as skew PBW extensions. We introduce the notion of $$\sigma $$ σ -filtered skew PBW extension and study some homological properties of these algebras. …”
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On <i>r</i>-Noncommuting Graph of Finite Rings by Rajat Kanti Nath, Monalisha Sharma, Parama Dutta, Yilun Shang

“…We characterize finite noncommutative rings such that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="sans-serif">Γ</mi><mi>R</mi><mi>r</mi></msubsup></semantics></math></inline-formula> is a tree, in particular a star graph. …”
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Equalizing ideal for integer-valued polynomials over the upper triangular matrix ring by Ali Reza Naghipour

“…Recently, integer-valued polynomials have been considered over some noncommutative rings (see for examples [3, 5, 6, 10]. In [1], Cahen and Chabert introduced the notion of equalizing ideal for a maximal ideal of $D$. …”
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