In this paper, we investigate various kinds of extensions of twin-good rings. Moreover, we prove that every element of an abelian neat ring R is twin-good if and only if R has no factor ring isomorphic to‌ Z2  or Z3. The main result of [24] states some conditions that any right self-injective ring R is twin-good. We extend this result to any regular Baer ring R by proving that every elemen...

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

In a 3D environment, motile cells accommodate their protruding and retracting activities to geometrical cues. Dictyostelium cells migrating on a perforated film explored its holes by forming actin rings around their border and extending protrusions through the free space. The response was initiated when an actin wave passed a hole, and the rings persisted only in the PIP3-rich territories surro...

Plants have numerous active protection strategies for adapting to complex and severe environments. These strategies provide endless inspiration for extending the service life of materials and machines. Tamarisk (Tamarix aphylla), a tree that thrives in raging sandstorm regions, has adapted to blustery conditions by evolving extremely effective and robust erosion resistant characteristics. Howev...

In the two anions of the title salt, C(2)H(10)N(2) (2+)·2C(8)H(5)N(8) (-)·2H(2)O, the central aromatic rings make dihedral angles of 13.53 (6) and 6.53 (7)° with the deprotonated tetra-zole rings, and 11.39 (6) and 10.41 (9)° with the other tetra-zole groups. In the crystal, the cations, anions and water mol-ecules are linked by an extensive O-H⋯N, N-H⋯O and N-H⋯N hydrogen-bond network into two...

let $r$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$ and $f(x)=a_0+a_1x+cdots+a_nx^n$ be a nonzero skew polynomial in $r[x;alpha]$. it is proved that if there exists a nonzero skew polynomial $g(x)=b_0+b_1x+cdots+b_mx^m$ in $r[x;alpha]$ such that $g(x)f(x)=c$ is a constant in $r$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $r$ such tha...

we observe some new characterizations of $n$-presented modules. using the concepts of $(n,0)$-injectivity and $(n,0)$-flatness of modules, we also present some characterizations of right $n$-coherent rings, right $n$-hereditary rings, and right $n$-regular rings.

in this paper, we introduce the concept of the   generalized aip-rings as a generalization of the generalized quasi-   baer rings   and generalized p.p.-rings. we show that the class of the generalized aip-rings is closed under direct products and morita invariance. we also characterize the 2-by-2 formal upper triangular matrix rings of this new class of rings. finally, we provide sever...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.