Unit (ring theory)

Abstract: We show that any pseudo MV-algebra is isomorphic with an interval Γ(G, u), where G is an l-group not necessarily Abelian with a strong unit u. In addition, we prove that the category of unital l-groups is categorically equivalent with the category of pseudo MV-algebras. Since pseudo MV-algebras are a non-commutative generalization of MV-algebras, our assertions generalize a famous result of Mundici for a representation of MV-algebras by Abelian unital l-groups. Our methods are completely different from those of Mundici. In addition, we show that any Archimedean pseudo MV-algebra is an MV-algebra.

Abstract: Let A be a finite-dimensional k-algebra (associative, with unit) over some fixed algebraically closed field k. Let mod A be the category of finitely generated left A-modules. With D = Homk(—,k) we denote the standard duality with respect to the ground field. Then A D(A A) is an injective cogenerator for mod A. For an arbitrary A-module A X we denote by proj.dimA X (resp. inj.dimA X) the projective dimension (resp. the injective dimension) of the module A X.

Abstract: Abstract Work gets done. Time passes. Careers— sequences of work experiences over time—unfold. A career depicts the person, the elementary unit in work arrangements. Careers invoke relationships within and among firms. Careers spell economic and social outcomes. Put simply, everyone who works has a career. And everyone’s life outside work is connected to the career. As lives are lived, a focus on careers, rather than on jobs, insists that we account for time and its implications. Careers matter!