Derivations, Jordan derivations, as well as automorphisms and Jordan automorphisms of the algebra of triangular matrices and some class of their subalgebras have been the object of active research for a long time [1, 2, 5, 6, 9, 10]. A well-know result of Herstein [11] states that every Jordan isomorphism on a prime ring of characteristic different from 2 is either an isomorphism or an anti-iso...

We prove the almost complete intersection case of the Lex-Plus-Powers Conjecture on graded Betti numbers. We show that the resolution of a lex-plus-powers almost complete intersection provides an upper bound for the graded Betti numbers of any other ideal with regular sequence in the same degrees and the same Hilbert function. A key ingredient is finding an explicit comparison map between two K...

During this search all rings are commutative and modules unitary. In we introduced the concept of Restrict Nearly semi-prime Sub-modules as generalization give some basic properties, examples charactarizations concepts stablished sufficient conditions on to be

Given a partial action α of a group G on an associative algebra A, we consider the crossed product A α G. Using the algebras of multipliers, we generalize a result of Exel (1997) on the associativity of A α G obtained in the context of C∗-algebras. In particular, we prove that A αG is associative, provided that A is semiprime. We also give a criterion for the existence of a global extension of ...

Frédéric Grosshans, Thomas Lawson, François Morain, and Benjamin Smith Laboratoire Aimé Cotton, CNRS, Univ. Paris-Sud, ENS Cachan, Université Paris-Saclay, 91405 Orsay, France LTCI — Télécom ParisTech, 23 avenue d’Italie, 75013, Paris, France École Polytechnique/LIX and Institut national de recherche en informatique et en automatique (INRIA) INRIA and École Polytechnique/LIX (Dated: November 16...