We solve two open problems concerning syntactic complexity: We prove that the cardinality of the syntactic semigroup of a left ideal or a suffix-closed language with n left quotients (that is, with state complexity n) is at most n n−1 + n − 1, and that of a two-sided ideal or a factor-closed language is at most n n−2 + (n − 2)2 n−2 + 1. Since these bounds are known to be reachable, this settles...

Abstract Proving statements about linear operators expressed in terms of identities often leads to finding elements certain form noncommutative polynomial ideals. We illustrate this by examples coming from actual operator and discuss relevant algorithmic methods for such polynomials based on Gröbner bases. In particular, we present algorithms computing the intersection a two-sided ideal with on...

We show that the quasiequational theory of a relatively congruence modular quasivariety of left R-modules is determined by a two-sided ideal in R together with a filter of left ideals. The two-sided ideal encodes the identities that hold in the quasivariety, while the filter of left ideals encodes the quasiidentities. The filter of left ideals defines a generalized notion of torsion. It follows...

It has been established by Inoue that a complex locally C*-algebra with a dense ideal posesses a bounded approximate identity which belonges to that ideal. It has been shown by Fritzsche that if a unital complex locally C*-algebra has an unbounded element then it also has a dense one-sided ideal. In the present paper we obtain analogues of the aforementioned results of Inoue and Fritzsche for r...

A right ideal A of a ring R is called annihilator-small if A+ T = R; T a right ideal, implies that l(T ) = 0; where l( ) indicates the left annihilator. The sum Ar of all such right ideals turns out to be a two-sided ideal that contains the Jacobson radical and the left singular ideal, and is contained in the ideal generated by the total of the ring. The ideal Ar is studied, conditions when it ...

In previous works we considered codes defined as ideals of quotients of non commutative polynomial rings, so called Ore rings of automorphism type. In this paper we consider codes defined as modules over non commutative polynomial rings, removing therefore some of the constraints on the length of the codes defined as ideals. The notion of BCH codes can be extended to this new approach and the c...

We introduce the notion of n -homoderivation on a ring id="M3"> ℜ and show that semiprime id="M4"> must have nontrivial central ideal if it admits an appropriate id="M5"> which is centralizing some one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.

Let L(H) be the ring of bounded operators on a separable Hubert space. Assuming the continuum hypothesis, we prove that in L(H) every two-sided ideal that contains an operator of infinite rank is the sum of two smaller two-sided ideals. The proof involves a new combinatorial description of ideals of L(H). This description is also used to deduce some related results about decompositions of ideal...