Let S = k[x1, . . . , xn] be a polynomial ring over a field k with n variables x1, . . . , xn, m the irrelevant maximal ideal of S, I a monomial ideal in S and I ′ the polarization of I in the polynomial ring S′ with ρ variables. We show that each graded piece H i m (S/I)a, a ∈ Z , of the local cohomology module H i m (S/I) is isomorphic to a specific graded pieceH i+ρ−n m ′ (S′/I )α, α ∈ Z , o...

We use Gröbner bases and a theorem of Handelman to show that an ideal I of R[x1, . . . , xk] contains a polynomial with positive coefficients if and only if no initial ideal inv(I), v ∈ R, has a positive zero. Let R = R[x1, . . . , xk], R = R[x1, . . . , xk] and, considering Laurent polynomials, let R̃ = R[x1 , . . . , xk ], R̃ = R[x ± 1 , . . . , x ± k ]. For a = (a1, . . . , ak) ∈ Z, write x = ...

we introduce the notions of t-dual rickart and strongly t-dual rickart modules. we provide several characterizations and investigate properties of each of these concepts. it is shown that every free (resp. finitely generated free) $r$-module is t-dual rickart if and only if $overline{z}^2(r)$ is a  direct summand of $r$ and end$(overline{z}^2(r))$ is a semisimple (resp. regular) ring. it is sho...

A generalization of injective modules (noted GI-modules), distinct from p-injective modules, is introduced. Rings whose p-injective modules are GI are characterized. If M is a left GI-module, E = End(AM), then E/J(E) is von Neumann regular, where J(E) is the Jacobson radical of the ring E. A is semisimple Artinian if, and only if, every left A-module is GI. If A is a left p. p., left GI-ring su...

Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M . In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following (i) d(U) ⊂ Z, (ii) d(U) ⊂ U and d(U) = 0, (iii) d(U) ⊂ U , d(U) ⊂ Z.

Transonic flows of a molecularly complex organic fluid through stator cascade were investigated by means large eddy simulations (LESs). The selected configuration was considered as representative the high-pressure stages high-temperature Organic Rankine Cycle (ORC) axial turbines, which may exhibit significant non-ideal gas effects. A heavy fluorocarbon, perhydrophenanthrene (PP11), working to ...

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 $m$...

A as a subset of Q[X], so, if I is an ideal of A, then QI is the ideal of Q[X] generated by I. Given a ring R, we denote the natural mapping A → A ⊗ R = R[X] by ι R. This note is devoted to the following algorithmic problem (see [1] for a definition and properties of Gröbner bases of ideals in polynomial rings over Z). Problem (P). Suppose that we have an infinite sequence f 1 , f 2 ,. .. of el...

Fix a Galois extension E/F of totally real number fields such that the Galois group G has exponent 2. Let S be a finite set of primes of F containing the infinite primes and all those which ramify in E, let SE denote the primes of E lying above those in S, and let OS E denote the ring of SE -integers of E. We then compare the Fitting ideal of K2(O E ) as a Z[G]-module with a higher Stickelberge...