let m be an artinian module over the commutative ring a (with nonzero identity) and a p spec a be such that a is a finitely generated ideal of a and am = m. also suppose that h = h where h. = m/ (0: a )for i

DNA protein cross-links (DPC), DNA interstrand cross-links (ISCL), and DNA single strand breaks following treatment of experimental ovarian tumor cells (O-342) with five new metal complexes (three platinum, one titanium, one ruthenium compounds) were investigated at 6, 24, and 48 h after drug exposure and compared with their in vitro growth inhibitory potential. cis-Diamminedichloroplatinum(II)...

A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

the author studies the $bf r$$g$-module $a$ such that $bf r$ is an associative ring‎, ‎a group $g$ has infinite section $p$-rank (or infinite 0-rank)‎, ‎$c_{g}(a)=1$‎, ‎and for every‎ ‎proper subgroup $h$ of infinite section $p$-rank (or infinite 0-rank respectively) the quotient module $a/c_{a}(h)$ is‎ ‎a finite $bf r$-module‎. ‎it is proved that if the group $g$ under‎ ‎consideration is local...

Let M be an Artinian module over the commutative ring A (with nonzero identity) and a p spec A be such that a is a finitely generated ideal of A and aM = M. Also suppose that H = H where H. = M/ (0: a )for i

The use of synthetic biological systems in research, healthcare, and manufacturing often requires autonomous history-dependent behavior and therefore some form of engineered biological memory. For example, the study or reprogramming of aging, cancer, or development would benefit from genetically encoded counters capable of recording up to several hundred cell division or differentiation events....

We show that finite-dimensional Lie algebras over a field of characteristic zero such that their high-degree cohomology in any finite-dimensional non-trivial irreducible module vanishes, are, essentially, direct sums of semisimple and nilpotent algebras. The classical First and Second Whitehead Lemmata state that the first, respectively second, cohomology group of a finite-dimensional semisimpl...

Let $(A,\mathfrak{m})$ be a Gorenstein local ring and let $M$, $N$ two Cohen-Macaulay $A$-modules with $M$ linked to via ideal $\mathfrak{q}$. $L$ another finitely generated $A$-module. We show that $\mathrm{Ext}^i_A(L,M) = 0 $ for all $i \gg 0$ if only $\mathrm{Tor}^A_i(L,N) 0$. If $D$ is module then we $\mathrm{Ext}^i_A(M, D) $\mathrm{Ext}^i_A(D^\dagger , N) 0$, where $D^\dagger \mathrm{Ext}^...