Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over finite fields. We generalize Lusztig’s results to reductive groups over arbitrary finite local rings. This generalization uses the Greenberg functor and the theor...

We define two classes of rings calling them weakly clean rings and weakly exchange rings both equipped with the strong property. Although the classes of weakly clean rings and weakly exchange rings are different, their two proper subclasses above do coincide. This extends results due to W. Chen (Commun. Algebra, 2006) and Chin-Qua (Acta Math. Hungar., 2011). We also completely characterize stro...

L-zero-divisor graphs of L-commutative rings have been introduced and studied in [5]. Here we consider L-zero-divisor graphs of a finite direct product of L-commutative rings. Specifically, we look at the preservation, or lack thereof, of the diameter and girth of the L-zirodivisor graph of a L-ring when extending to a finite direct product of L-commutative rings.

In the title compound, C(13)H(11)NO(2), the aromatic rings are oriented at a dihedral angle of 42.52 (12)°. The crystal structure is stabilized by inter-molecular N-H⋯O hydrogen bonds, which form infinite one-dimensional polymeric chains extending along the a axis. C-H⋯π inter-actions between the aromatic rings are also present.

The title compound, C16H14N4, is non-planar with dihedral angles between the planes of the imidazole and phenyl-enedi-amine rings of 30.66 (4)° and between the planes of the phenyl-enedi-amine and N-phenyl rings of 56.63 (7)°. In the crystal, mol-ecules are connected by N-H⋯N hydrogen bonds, generating a chain extending along the b-axis direction. The crystal structure is also stabilized by C-H...

Abstract The class of good semigroups is a subsemigroups $${\mathbb {N}}^h$$ N h , that includes the value rings associated to curve singularities and their blowups, allows study combinatorically properties these rings. In this paper we give chara...