Related papers: Morita cancellation problem
We study Zariski cancellation problem for noncommutative algebras that are not necessarily domains.
In this article, we discuss some recent developments of the Zariski Cancellation Problem in the setting of noncommutative algebras and Poisson algebras.
We characterize the inverse semigroups that are Morita equivalent to graph inverse semigroups. We also consider a generalization to inverse semigroups associated with left cancellative categories.
A noncommutative analogue of the Zariski cancellation problem asks whether $A[x]\cong B[x]$ implies $A\cong B$ when $A$ and $B$ are noncommutative algebras. We resolve this affirmatively in the case when $A$ is a noncommutative finitely…
In this article, we shall discuss the solution to the Zariski Cancellation Problem in positive characteristic, various approaches taken so far towards the possible solution in characteristic zero, and several other questions related to this…
We study both Morita cancellative and skew cancellative properties of noncommutative algebras as initiated recently in several papers and explore that which classes of noncommutative algebras are Morita cancellative (respectively, skew…
We study a noncommutative version of the Zariski cancellation problem for some classes of connected graded Artin-Schelter regular algebras of global dimension three.
We discuss different generalizations of Zariski decomposition, relations between them and connections with finite generation of divisorial algebras.
In this note we use the divisorial Zariski decomposition to give a more intrinsic version of the algebraic Morse inequalities.
We study the Zariski cancellation problem for Poisson algebras in three variables. In particular, we prove those with Poisson bracket either being quadratic or derived from a Lie algebra are cancellative. We also use various Poisson algebra…
This is an expanded version of the talk by the author at the conference Polynomial Rings and Affine Algebraic Geometry, February 12--16, 2018, Tokyo Metropolitan University, Tokyo, Japan. Considering a local version of the Zariski…
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
We study Morita equivalence in the context of quantales with identity, in the wake of Katsov and Nam's analogous work on semirings. Among a number of other results, we prove a characterization of Morita equivalence and an…
In this paper we present some key moments in the history of Morita equivalence for operator algebras.
We consider a variant of the notion of Morita equivalence appropriate to weak* closed algebras of Hilbert space operators, which we call {\em weak Morita equivalence}. We obtain new variants, appropriate to the dual algebra setting, of the…
Let $L$ be a quantum semigroupoid, more precisely a $\times_R$-bialgebra in the sense of Takeuchi. We describe a procedure replacing the algebra $R$ by any Morita equivalent, or in fact more generally any $\sqrt{\text{Morita}}$ equivalent…
Logicians and philosophers of science have proposed various formal criteria for theoretical equivalence. In this paper, we examine two such proposals: definitional equivalence and categorical equivalence. In order to show precisely how…
We consider how Morita equivalences are compatible with the notion of a corner subring. Namely, we outline a canonical way to replace a corner subring of a given ring with one which is Morita equivalent, and look at how such an equivalence…
In this paper we fully solve the Morita equivalence problem for symplectic reflection algebras associated to direct products of finite subgroups of $SL_2(\mathbb{C})$. Namely, given a pair of such symplectic reflection algebras $H_c,…
The Zariski cancellation problem plays a central role in affine algebraic geometry and noncommutative algebra, with locally nilpotent derivations providing a fundamental invariant-theoretic approach. This article presents a unified survey…