let $ m , n in mathbb{n}$, $d$ be a division ring, and $m_{m times n}(d)$ denote the bimodule of all $m times n$ matrices with entries from $d$. first, we characterize one-sided submodules of $m_{m times n}(d)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $d$. next, we introduce the notion of a nest module of matrices with entries from $d$. we ...

Let A be a left and right noetherian ring We denote by Amod the abelian category of nitely generated left A modules and by Aproj the category of nitely generated projective left A modules We de note by R A the Grothendieck group of Amod and by R A the Grothendieck group of Aproj If X is an object of Amod resp of Aproj we denote by X its representative in R A resp in R A We denote by modA the ab...

1 Description The method of Grr obner bases in commutative polynomial rings introduced by Buchberger (e.g. 1]) is a well-known and very important tool in polynomial ideal theory, for example in solving the ideal membership problem. XIDEAL extends the method to exterior algebras using algorithms from 2]. There are two main departures from the commutative polynomial case. First, owing to the non-...

Let R be a commutative ring with identity. Let φ : I(R) → I(R) ∪ {∅} be a function where I(R) denotes the set of all ideals of R. A proper ideal Q of R is called φ-primary if whenever a, b ∈ R, ab ∈ Q−φ(Q) implies that either a ∈ Q or b ∈ √ Q. So if we take φ∅(Q) = ∅ (resp., φ0(Q) = 0), a φ-primary ideal is primary (resp., weakly primary). In this paper we study the properties of several genera...

We study conditions on a C∗-dynamical system (A,G,α) under which induction of primitive ideals (resp. irreducible representations) from stabilizers for the action of G on the primitive ideal space Prim(A) give primitive ideals (resp. irreducible representations) of the crossed product A⋊α G. The results build on earlier results of Sauvageot [17] and others, and will correct a (possibly overly o...

We classify, in terms of the structure finite group G, all algebras KG for which right ideals are annihilators principal left ideals. This means language coding theory that we classify code-checkable have been considered so far only abelian groups G. Optimality checkable codes and asymptotic results discussed.

Let S be a harmonic extension of an H -type group and call δ its modular function. We find sufficient conditions on the spherical transform of a radial distribution k on S , so that δ−zk is a left [resp. a right] convolutor of L(S) , 1 < p < ∞ , for every complex z with 0 ≤ Rez ≤ 1 [resp. −1 + 1/p ≤ Rez ≤ 1/p ].

Let S be a harmonic extension of an H-type group and call its modular function. We nd suucient conditions on the spherical transform of a radial distribution k on S, so that ?z k is a left resp. a right] convolutor of L p (S), 1 < p < 1, for every complex z with 0 Rez 1 resp. ?1 + 1=p Rez 1=p].

In this paper, we discuss the hypothesis that an ordered Γ-semigroup can be constructed on M-left(right)-tri-basis. order to generalize left(right)-tri-basis using Γ-semigroups and semigroups, examined M-tri-ideals from a purely algebraic standpoint. We also present form of M-tri-ideal generator. investigated M-left(right)-tri-ideal Γ-semigroup. obtain their properties, used It was possible gen...