3 citations · 4 across the 6 of their papers we have counts for
7 papers
The ozone group of
James Gómez, Helbert Venegas
We determine the ozone group of \(U_q^{+}(B_2)\). More precisely, if \(\ell=\operatorname{ord}(q^2)\) when \(q\) is a root of unity, we obtain $$ \operatorname{Oz}(U_q^{+}(B_2)) \c…
The ozone groups of the algebras
James Gómez, Helbert Venegas
Let be a primitive -th root of unity, , and let be a nonzero polynomial such that for every $j\in\supp(f)$. Set $e=\gcd(n,\{j+1:j\in\supp(f)\})$. We s…
Cancellation problem via locally nilpotent derivations
César F. Venegas R., Helbert J. Venegas R
The Zariski cancellation problem plays a central role in affine algebraic geometry and noncommutative algebra, with locally nilpotent derivations providing a fundamental invariant-…
The center of the total ring of fractions
Oswaldo Lezama, Helbert Venegas
Let be a right Ore domain, be the center of and be the right total ring of fractions of . If is a field and is a -algebra, in this short paper…
Gelfand-Kirillov dimension for rings
Oswaldo Lezama, Helbert Venegas
The classical Gelfand-Kirillov dimension for algebras over fields has been extended recently by J. Bell and J.J Zhang to algebras over commutative domains. However, the behavior of…
Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin, and Heinzer
Jason P. Bell, Maryam Hamidizadeh, Hongdi Huang +1
Let be a field and let be a finitely generated -algebra. The algebra is said to be cancellative if whenever is another -algebra with the property that $A[x]\c…
Center of skew PBW extensions
José Oswaldo Lezama Serrano, Helbert Javier Venegas Ramírez
In this paper we compute the center of many noncommutative algebras that can be interpreted as skew extensions. We show that, under some natural assumptions on the parameters…