http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Sun, 12 May 2013 13:54:14 +0000 http://www.hindawi.com/journals/algebra/2013/128064/ This paper is a survey about recent progress on submersive morphisms of schemes combined with new results that we prove. They concern the class of quasicompact universally subtrusive morphisms that we introduced about 30 years ago. They are revisited in a recent paper by Rydh, with substantial complements and key results. We use them to show Artin-Tate-like results about the 14th problem of Hilbert, for a base scheme either Noetherian or the spectrum of a valuation domain. We look at faithfully flat morphisms and get “almost” Artin-Tate-like results by considering the Goldman (finite type) points of a scheme. Bjorn Poonen recently proved that universally closed morphisms are quasicompact. By introducing incomparable morphisms of schemes, we are able to characterize universally closed surjective morphisms that are either integral or finite. Next we consider pure morphisms of schemes introduced by Mesablishvili. In the quasicompact case, they are universally schematically dominant morphisms. This leads us to a characterization of universally subtrusive morphisms by purity. Some results on the schematically dominant property are given. The paper ends with properties of monomorphisms and topological immersions, a dual notion of submersions. Gabriel Picavet Copyright © 2013 Gabriel Picavet. All rights reserved. Tue, 16 Apr 2013 08:14:47 +0000 http://www.hindawi.com/journals/algebra/2013/107265/ The cyclic graph of a finite group is as follows: take as the vertices of and join two distinct vertices and if is cyclic. In this paper, we investigate how the graph theoretical properties of affect the group theoretical properties of . First, we consider some properties of and characterize certain finite groups whose cyclic graphs have some properties. Then, we present some properties of the cyclic graphs of the dihedral groups and the generalized quaternion groups for some . Finally, we present some parameters about the cyclic graphs of finite noncyclic groups of order up to . Xuan Long Ma, Hua Quan Wei, and Guo Zhong Copyright © 2013 Xuan Long Ma et al. All rights reserved. Wed, 10 Apr 2013 09:59:33 +0000 http://www.hindawi.com/journals/algebra/2013/368962/ The notion of intersectional soft subalgebras of a BE-algebra is introduced, and related properties are investigated. Characterization of an intersectional soft subalgebra is discussed. The problem of classifying intersectional soft subalgebras by their inclusive subalgebras will be solved. Young Bae Jun and Sun Shin Ahn Copyright © 2013 Young Bae Jun and Sun Shin Ahn. All rights reserved. Mon, 25 Mar 2013 10:17:40 +0000 http://www.hindawi.com/journals/algebra/2013/460582/ We provide a recipe for “fattening” a category that leads to the construction of a double category. Motivated by an example where the underlying category has vector spaces as objects, we show how a monoidal category leads to a law of composition, satisfying certain coherence properties, on the object set of the fattened category. Saikat Chatterjee, Amitabha Lahiri, and Ambar N. Sengupta Copyright © 2013 Saikat Chatterjee et al. All rights reserved. Thu, 21 Mar 2013 14:37:38 +0000 http://www.hindawi.com/journals/algebra/2013/794054/ We study the case of a real homogeneous polynomial whose minimal real and complex decompositions in terms of powers of linear forms are different. We prove that if the sum of the complex and the real ranks of is at most , then the difference of the two decompositions is completely determined either on a line or on a conic or two disjoint lines. Edoardo Ballico and Alessandra Bernardi Copyright © 2013 Edoardo Ballico and Alessandra Bernardi. All rights reserved. Wed, 20 Mar 2013 14:28:34 +0000 http://www.hindawi.com/journals/algebra/2013/483949/ Regular -crystals are certain edge-colored directed graphs, which are related to representations of the quantized universal enveloping algebra . For such a crystal with colors , we consider its maximal connected subcrystals with colors and with colors and characterize the interlacing structure for all pairs of these subcrystals. This enables us to give a recursive description of the combinatorial structure of via subcrystals and develop an efficient procedure of assembling . Vladimir I. Danilov, Alexander V. Karzanov, and Gleb A. Koshevoy Copyright © 2013 Vladimir I. Danilov et al. All rights reserved. Wed, 20 Mar 2013 09:23:30 +0000 http://www.hindawi.com/journals/algebra/2013/581023/ Piecewise prime (PWP) module is defined in terms of a set of triangulating idempotents in . The class of PWP modules properly contains the class of prime modules. Some properties of these modules are investigated here. M. Gurabi Copyright © 2013 M. Gurabi. All rights reserved.