It is well-known that the set of h -terms modulo &-convertibility is a semi-group with I as identity element and composition 0, defined by M 0 N = BMN, where B = hxyt . x(yz). In [6, pp. 167,168] the question is raised under what conditions an element in this semi-group has an inverse. DezanXiancaglini gave in [8] a characterization of (w.r.t. A&-calculus) invertible terms having a normal form ...

We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a finite set S of invertible substitutions such that any invertible substitution can be written as Iw ◦ σ1 ◦ σ2 ◦ · · · ◦ σk, where Iw is the inner automorphism associated with w, and σj ∈ S for 1 ≤ j ≤ k. As a consequence, M is the matrix of an invertible substitution if and only if it is a f...

If a and b are elements of an algebra, then we show that ab is Drazin invertible if and only if ba is Drazin invertible. With this result we investigate products of bounded linear operators on Banach spaces. 1. Drazin inverses Throughout this section A is a real or complex algebra with identity e 6= 0. We denote the group of invertible elements of A by A. We call an element a ∈ A relatively reg...

We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on classical tilings plane due to Raphael Robinson. Extending those group by exploiting group’s structure and posing additional local rules prune out remaining periodic behavior, we maintain rich projective subdynamics Z2 cosets. In addition, obtained factors onto aperiodic...

In this paper, we introduce fuzzy Banach algebra and study the properties of invertible elements and its relation with opensets. We obtain some interesting results.

Given a Laurent polynomial over flat $$\mathbf {Z}$$ -algebra, Vlasenko defines formal group law. We identify this law with coordinate system of functor. When the “Hasse–Witt matrix” is invertible, matrix by taking certain $$p$$ -adic limit. show that Frobenius Dieudonné module modulo .

Forming real vector spaces, we have the linear maps, which preserve the vector space structure L(n; R) = { M : R → R ∣∣M(a~x+ b~y) = aM(~x) + bM(~y) } (1) This is a monoid, not a group, as inverses may not exist. The first group is the general linear group, which preserve dimensionality GL(n; R) = { M ∈ L(n) ∣∣M is invertible } . (2) Further, we have the area preserving maps SL(n; R) = { M ∈ L(...

Invertible almost invariant sets The rst problem is in our treatment of almost invariant sets which are invertible (see De nition 2.12). Before discussing the details, we need to brie y recall the construction in chapter 3. We have a nitely generated group G with nitely generated subgroups H1; : : : ; Hn and, for 1 i n, we have a nontrivial Hi{almost invariant subset Xi of G. Recall that E deno...

Abstract We prove the existence of a full exceptional collection for derived category equivariant matrix factorizations an invertible polynomial with its maximal symmetry group. This proves conjecture Hirano–Ouchi. In Gorenstein case, we also stronger version this due to Takahashi. Namely, that is strong.