Generalized Rainich conditions, generalized stress–energy conditions, and the Hawking–Ellis classification

Group rings satisfying generalized Engel conditions

Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1)  y]=[[x ,_( n)  y]  , y]. In this paper we show that necessary and sufficient conditions for RG to satisfies [x^m(x,y)   ,_( n(x,y))  y]=0 is: 1) if r is a power of a prime p, then G is a locally nilpotent group an...

Moufang-like conditions for generalized quadrangles and classification of all finite quasi-transitive generalized quadrangles

We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...

Common Fixed Point Theorms Using Generalized Contractive Conditions

Generalized Calderón Conditions and Regular Orbit Spaces

The construction of generalized continuous wavelet transforms on locally compact abelian groups A from quasi-regular representations of a semidirect product group G = A ⋊ H acting on L(A) requires the existence of a square-integrable function whose Plancherel transform satisfies Calderón-type resolution of the identity. The question then arises under what conditions such square-integrable funct...

On Comparability Conditions and Generalized Valuation Maps

In this study, we generalize the comparability conditions, addressed in Comparability of ideals and valuation over rings [2], between certain maximal ideals and fractional ideals of D which also force D to be a quasi-local domain. Also, we introduce the notion of an almost totally ordered group and establish that: “An integral domain D is an AVD if and only if the group of divisibility of D is ...