Canonical orders, introduced in the minimal model program for orders [CI05], are simultaneous generalisations of Kleinian singularities k[[s, t]], G < SL2 and their associated skew group rings k[[s, t]]∗G. In this paper, we construct minimal resolutions of canonical orders via non-commutative cyclic covers and skew group rings. This allows us to exhibit a derived equivalence between minimal res...

The paper studies the following question: Given a ring R, when does the zero-divisor graph (R) have a regular endomorphism monoid? We prove if R contains at least one nontrivial idempotent, then (R) has a regular endomorphism monoid if and only if R is isomorphic to one of the following rings: Z2 × Z2 × Z2; Z2 × Z4; Z2 × (Z2[x]/(x)); F1 × F2, where F1, F2 are fields. In addition, we determine a...

We show that the skew-growth function of a dual Artin monoid of finite type P has exactly rank(P ) =: l simple real zeros on the interval (0, 1]. The proofs for types Al and Bl are based on an unexpected fact that the skewgrowth functions, up to a trivial factor, are expressed by Jacobi polynomials due to a Rodrigues type formula in the theory of orthogonal polynomials. The skew-growth function...

A Leavitt labelled path algebra over a commutative unital ring is associated with space, generalizing algebras graphs and ultragraphs as well torsion-free generated by idempotents. We show that can be realized partial skew group rings, Steinberg algebras, Cuntz-Pimsner algebras. Via these realizations we obtain generalized uniqueness theorems, description of diagonal preserving isomorphisms cha...

1 Rings Definition 1.1 (Rings). A ring R is a set with two binary operations + and · called addition and multiplication respectively such that: (1) (R, +) is an Abelian group with identity element 0. (2) (R, ·) is a monoid with identity element 1. (3) Multiplication distributes over addition: a · (b + c) = a · b + a · c and (b + c) · a = b · a + c · a for all a, b, c ∈ R. A ring is called commu...

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto powerseries rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of...

Groups can be studied using methods from diierent elds such as combina-torial group theory or string rewriting. Recently techniques from Grr obner basis theory for free monoid rings (non-commutative polynomial rings) respectively free group rings have been added to the set of methods due to the fact that monoid and group presentations (in terms of string rewriting systems) can be linked to spec...

We study the interaction between various analytification functors, and a class of morphisms rings, called homotopy epimorphisms. An functor assigns to simplicial commutative algebra over ring $R$, along with choice Banach structure on monoid in monoidal model category ind-Banach $R$-modules. show that several analytifications relevant analytic geometry - such as Tate, overconvergent, Stein anal...