Automorphisms of Incidence Algebras

Linear Algebra and its Applications

Linear Algebra and its Applications, 1989

International Journal of Mathematics and Mathematical Sciences, 2002

The incidence algebraI(X,ℝ)of a locally finite poset(X,≤)has been defined and studied by Spiegel and…

Notre Dame Journal of Formal Logic, 1973

International Journal of Mathematics and Mathematical Sciences, 2005

International Journal of Mathematics and Mathematical Sciences, 2004

Let X, X′ be two locally finite, preordered sets and let R be any indecomposable commutative ring. The incidence algebra I(X,R), in a sense, represents X, because of the well-known result that if the rings I(X,R) and I(X′,R) are isomorphic, then X and X′ are isomorphic. In this paper, we consider a preordered set X that need not be locally finite but has the property that each of its equivalence classes of equivalent elements is finite. Define I*(X,R) to be the set of all those functions f:X×X→R such that f(x,y)=0, whenever x⩽̸y and the set Sf of ordered pairs (x,y) with x<y and f(x,y)≠0 is finite. For any f,g∈I*(X,R), r∈R, define f+g, fg, and rf in I*(X,R) such that (f+g)(x+y)=f(x,y)+g(x,y), fg(x,y)=∑x≤z≤yf(x,z)g(z,y), rf(x,y)=r⋅f(x,y). This makes I*(X,R) an R-algebra, called the weak incidence algebra of X over R. In the first part of the paper it is shown that indeed I*(X,R) represents X. After this all the essential one-sided ideals of I*(X,R) are determined and the maximal r...

Discrete Mathematics, 1979

The Third Millennium is arguably the most formative period in Mesopotamian History. Its historical and cultural processes lay the groundwork for the development of later Ancient Near Eastern civilizations. While Third Millennium text corpora may be broad and diverse, they often present similar problems that call for shared solutions. Unfortunately, the complex and fragmentary nature of the documentation is also known to attract less attention compared to later periods, leaving space for a new impulse in the field. This is the foreground of the organization of this session, the third in a series of thematic workshops on third millennium studies at the Rencontre Assyriologique Internationale – the first two were held in Paris 2019 and Leiden 2023. After a reassessment of the current research in Third Millennium studies, the speakers will briefly present their original research as an introduction to the workshop. Armando Bramanti will present his current work on text editions, with particular regard to Latin American collections. Angela Greco will offer an overview of her research on the exploitation and management of natural resources in the southernmost Mesopotamian landscape. To conclude, Géraldine Mastelli will bring attention to a selection of Urukagina’s fish offering lists challenging the notion of ki-en-gi in Early Dynastic Sumer. Location: 69th RAI, Helsinki. Event date: July 8-12, 2024

International Journal of Advances in Materials Science and Engineering (IJAMSE) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Materials Science and Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of Materials Science and Engineering.