Communications in Algebra

Bani-Ata, Mashhour Alali

doi: 10.1080/00927870802055760pmid: N/A

The aim of this article is to investigate all semifields A of order q 4 where q is a power of 2, having the properties that A contains GF(q 2) in its left nucleus and admits a four-group E ≅ Z 2 × Z 2 of automorphisms of A acting freely on A.

Cho, Eun-Hee; Oh, Sei-Qwon

doi: 10.1080/00927870802068367pmid: N/A

Let A have a locally finite and multiparameter indexed filtration ℱ, and let B be a homomorphic image of A. Thus B has the locally finite and multiparameter indexed filtration induced from ℱ. Here we study a relation between the associated graded algebra of A and that of B and use this result to calculate the Gelfand–Kirillov dimension of several algebras related to quantized algebras and Poisson enveloping algebras.

Wei, Jiaqun

doi: 10.1080/00927870802068383pmid: N/A

Let R be an exchange ring. In this article, we show that the following conditions are equivalent: (1) R has stable range not more than n; (2) whenever x ∈ R n is regular, there exists some unimodular regular w ∈  n R such that x = xwx; (3) whenever x ∈ R n is regular, there exist some idempotent e ∈ R and some unimodular regular w ∈ R n such that x = ew; (4) whenever x ∈ R n is regular, there exist some idempotent e ∈ M n (R) and some unimodular regular w ∈ R n such that x = we; (5) whenever a( n R) + bR = dR with a ∈ R n and b,d ∈ R, there exist some z ∈ R n and some unimodular regular w ∈ R n such that a + bz = dw; (6) whenever x = xyx with x ∈ R n and y ∈  n R, there exist some u ∈ R n and v ∈  n R such that vxyu = yx and uv = 1. These, by replacing unimodularity with unimodular regularity, generalize the corresponding results of Canfell (1995, Theorem 2.9), Chen (Chen 2000, Theorem 4.2 and Proposition 4.6, Chen 2001, Theorem 10), and Wu and Xu (1997, Theorem 9), etc.

Maginnis, John; Onofrei, Silvia

doi: 10.1080/00927870802069795pmid: N/A

We define new collections of p-subgroups for a finite group G and p a prime dividing its order. We study the homotopy relations among them and with the standard collections of p-subgroups and determine their ampleness and sharpness properties.

Moghaddam, Mohammad Reza R.; Salemkar, Ali Reza; Karimi, Taghi

doi: 10.1080/00927870802070033pmid: N/A

Let (H, N) be a pair of finite p-groups, in which N is a normal subgroup of H. In the present article, some upper bounds for the order of the commutator subgroup [N, H] are given. It is also constructed an upper bound for the order of the Schur multiplier of the pair of finite p-groups.

Tang, Xilin

doi: 10.1080/00927870802070074pmid: N/A

A class 𝒱 of regular semigroups is an e-variety if it is closed under homomorphic images, regular subsemigroups, and direct products. Let S be a regular semigroup and S° an inverse subsemigroup of S. Then S° is called an “inverse transversal of S” if it contains a unique inverse x° of each element x of S. Many important classes of regular semigroups form e-varieties of regular semigroups. However, the class of regular semigroups with inverse transversals does not form an e-variety. In this article, we consider a regular semigroup S with an inverse transversal S° as a regular unary semigroup (S, ○) with a regular unary operation “○” on S firstly. Then we prove that S is a regular semigroup with an inverse transversal S° if and only if (S, ○) satisfies the following identities (IST): Such a regular operation is called an “ist-operation,” and a regular semigroup S is called an “ist-semigroup” if there exists an ist-operation “○” on S. A regular subsemigroup T of a regular semigroup S is called an “ist-subsemigroup” if T is an ist-semigroup. A class 𝒱 of ist-semigroups is an ist-variety if it is closed under homomorphic images, ist-subsemigroups, and direct products. We characterize the set of identities of (IST) and investigate the relationship among those identities. Also, we describe the classes of regular unary semigroups which satisfy some of these identities in (IST). On the basis of that, we'll characterize the ist-varieties, in a later article.

Bamberg*, John; Penttila**, Tim

doi: 10.1080/00927870802070108pmid: N/A

We use a theorem of Guralnick, Penttila, Praeger, and Saxl to classify the subgroups of the general linear group (of a finite dimensional vector space over a finite field) which are overgroups of a cyclic Sylow subgroup. In particular, our results provide the starting point for the classification of transitive m-systems; which include the transitive ovoids and spreads of finite polar spaces. We also use our results to prove a conjecture of Cameron and Liebler on irreducible collineation groups having equally many orbits on points and on lines.

Muchtadi-Alamsyah, Intan

doi: 10.1080/00927870802070165pmid: N/A

We construct an action of a braid group associated to a complete graph on the derived category of a certain symmetric Nakayama algebra which is also a Brauer star algebra with no exceptional vertex. We connect this action with the affine braid group action on Brauer star algebras defined by Schaps and Zakay–Illouz. We show that for Brauer star algebras with no exceptional vertex, the action is faithful.

Žemlička, Jan

doi: 10.1080/00927870802070207pmid: N/A

A module M is called “self-small” if the functor Hom(M, −) commutes with direct sums of copies of M. The main goal of the present article is to construct a non-self-small product of self-small modules without nonzero homomorphisms between distinct ones and to correct an error in a claim about products of self-small modules published by Arnold and Murley in a fundamental article on this topic. The second part of the article is devoted to the study of endomorphism rings of self-small modules.

Arenas-Carmona, Luis

doi: 10.1080/00927870802070405pmid: N/A

We give a cohomological characterization of the set of conjugacy classes of finite subgroups of the projective multiplicative group of a finite dimensional algebra that become conjugate to a given group over some finite separable extension of the base field. We provide two applications.