Journal of Algebra and Its Applications

The aim of this paper is to provide a proof of the following result claimed by Albu (Infinite field extensions with Galois–Cogalois correspondence (II), Revue Roumaine Math. Pures Appl. 47 (2002), to appear): The Kneser group Kne(E/F) of an Abelian G-Cogalois extension E/F and the group of continuous characters Ch(Gal(E/F)) of its Galois group Gal(E/F) are isomorphic (in a noncanonical way). The proof we give in this paper explains why such an isomorphism is expected, being based on a classical result of Baer (Amer. J. Math.61 (1939), 1–44) devoted to the existence of group isomorphisms arising from lattice isomorphisms of their lattices of subgroups.

This paper takes a detailed look at a subject that occurs in various contexts in mathematics, the fixed-point sets of torus actions on flag manifolds, and considers it from the (perhaps nontraditional) perspective of moment maps and length functions on Weyl groups. The approach comes from earlier work of the author where it is shown that certain singular flows in the Hamiltonian system known as the Toda lattice generate the action of a group A on a flag manifold, where A is a direct product of a non-maximal torus and unipotent group. As a first step in understanding the orbits of A in connection with the Toda lattice, this paper seeks to understand the fixed points of the non-maximal tori in this setting.

Let G be a finite group. Based on the prime graph of G, the order of G can be divided into a product of coprime positive integers. These integers are called order components of G and the set of order components is denoted by OC(G). Some non-abelian simple groups are known to be uniquely determined by their order components. In this paper we prove that almost sporadic simple groups, except Aut(J₂) and Aut(McL), and the automorphism group of PSL(2, 2ⁿ) where n=2^s are also uniquely determined by their order components. Also we discuss about the characterizability of Aut(PSL(2, q)). As corollaries of these results, we generalize a conjecture of J. G. Thompson and another conjecture of W. Shi and J. Bi for the groups under consideration.

Essential ideals of multiplicatively semiprime algebras are themselves multiplicatively semiprime algebras and memorize the extended centroid.

In the present paper, modules which are subisomorphic (in the sense of Goldie) to their pure-injective envelopes are studied. These modules will be called almost pure-injective modules. It is shown that every module is isomorphic to a direct summand of an almost pure-injective module. We prove that these modules are ker-injective (in the sense of Birkenmeier) over pure-embeddings. For a coherent ring R, the class of almost pure-injective modules coincides with the class of ker-injective modules if and only if R is regular. Generally, the class of almost pure-injective modules is neither closed under direct sums nor under elementary equivalence. On the other hand, it is closed under direct products and if the ring has pure global dimension less than or equal to one, it is closed under reduced products. Finally, pure-semisimple rings are characterized, in terms of almost pure-injective modules.

In [5], Miyashita introduced tilting modules of finite projective dimension. A tilting module _AV of projective dimension less or equal than r furnishes r + 1 equivalences between subcategories of A-Mod and End V-Mod: we call static and costatic the modules in A-Mod and End V-Mod, respectively, involved in these equivalences. In this paper we characterize the modules in A-Mod and End V-Mod which have a filtration with static and costatic factors, respectively.

Let R anf T be rings, and let U be a faithful R-T-bimodule. We show that the triple (R, U, T) has a Morita duality if and only if _RR and T_T are linearly compact, and there is a duality between the semisimple factors R/J(R) and T/J(T) induced by the socle of U.

The main tool to prove this result is proving that lattice anti-isomorphisms can be patched together provided the AB-5* condition is satisfied.

The natural map of K-spectra K(R) → G(R) fits into a homotopy cofibre sequence

Let L be a finitely generated free color Lie superalgebra. We obtained a criterion in terms of invertibility of the double Jacobian matrix associated with a special element for a given endomorphism of L to be an automorphism.

We derive explicit formulae for the characteristics H^(k) of the semiregular nilpotent orbits D_n(a_k) of the simple complex Lie algebra of type D_n. These formulae express H^(k) as an integral linear combination of a basis of the Cartan subalgebra of . For that purpose we use several suitable bases of consisting of coroots. We also construct several explicit standard triples (E, H, F) with H = H^(k), and E, F ∈ D_n(a_k). Similar triples are constructed also for each connected component of the intersection of the orbit D_n(a_k) with the split real form and the real form of .