Let $${\cal M}$$ be an n-cluster tilting subcategory of mod-Λ, where Λ is Artin algebra. S}({\cal M})$$ denote the full S}(\Lambda )$$ , submodule category Λ, consisting all monomorphisms in . We construct two functors from to $$\bmod - \underline {\cal M} $$ finitely presented additive contravariant on stable show that these are full, dense and objective hence provide equivalences between quot...

Take for instance a k-algebra 4 over a field k. Then the usual k-dual DM=Homk(M, k) of a finite dimensional 4-module M satisfies all three properties. However for infinite dimensional 4-modules the condition (D1) does not hold, and for most rings there is even on the level of the finite length modules no duality functor between right and left modules available. The aim of this note is to descri...

Let K be a perfect field of characteristic p > 0, A1 := K〈x, ∂ | ∂x−x∂ = 1〉 be the first Weyl algebra and Z := K[X := x, Y := ∂] be its centre. It is proved that (i) the restriction map res : AutK(A1) → AutK(Z), σ 7→ σ|Z , is a monomorphism with im(res) = Γ := {τ ∈ AutK(Z) | J (τ) = 1} where J (τ) is the Jacobian of τ (note that AutK(Z) = K ∗ ⋉ Γ and if K is not perfect then im(res) 6= Γ); (ii)...

The case for a recent expansion of modern humans from Africa has been strengthened by the finding of monomorphism in part of a Y-linked gene, consistent with the low variability seen in human mitochondrial DNAs.

Aims: To Analysis of genetic variability in Tulsi (Ocimum sanctum) genotypes by using RAPD & SSR Markers.
 Place and Duration Study: Department Plant Biotechnology at K.K.Wagh College Agricultural Biotechnology, Nashik.
 Methodology: Ocimum tenuiflorum Linn., commonly known as Tulsi, is an aromatic plant with significant traditional medicinal value. assess the diversity relatednes...

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...