We introduce a notion of highly Kummer-faithful fields and study its relationship with the fields. also give some examples For example, if $k$ is number field finite degree over \mathbb{Q}, $g$ an integer $> 0$ $\mathbf{m}=(m_p)_p$ family non-negative integers, where $p$ ranges all prime numbers, then extension $k_{g,\mathbf{m}}$ obtained by adjoining to coordinates elements $p^{m_p}$-torsion s...

Spatial release from masking refers to a benefit for speech understanding. It occurs when a target talker and a masker talker are spatially separated. In those cases, speech intelligibility for target speech is typically higher than when both talkers are at the same location. In cochlear implant listeners, spatial release from masking is much reduced or absent compared with normal hearing liste...

The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $Nleq_{sd}M$, if for any index set $I$, $prod _{I}Nleq_{d}prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'bi...

in this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.

We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced in [KLS08]. We generalize the central extension theorem of Buhler and Reichstein, [BR97, Theorem 5.3] and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev [KM08] about the essential dimen...