Automorphism-invariant modules have emerged as a linchpin in the study of modern algebra, especially in the context of module theory over noncommutative rings. These modules are defined by the ...

Informally, a dynamic system is any physical system that evolves with time (e.g., a pendulum, a planet orbiting the sun, the weather, etc). From a more mathematically precise perspective, one can ...

Let Γ be the automorphism group of a nonelementary reduced abelian p-group, p ≥ 5. It is shown that every noncentral normal subgroup of Γ contains a noncentral elementary abelian normal p-subgroup of ...

The classification of normal singular cubic surfaces in P³ over a complex number field C was given by J. W. Bruce and C. T. C. Wall. In this paper, first we prove their results by a different way, ...