It has long been recognized that tuberculous cavities may occur in the apex of the lower lobe of the lung, often known as the dorsal lobe (Kidd, 1886; Fowler, 1888 ; Sweany and others, 1931). Steen (1945) has reviewed the many publications on basal tuberculosis, but no paper I have traced has been concerned exclusively with tuberculous cavities of the dorsal lobe; most authors do not differenti...

We give a purely algebraic proof of the hypersurface case of the Toric Residue Mirror Conjecture recently proposed by Batyrev and Materov.

In this survey, we discuss two research areas related to Massey’s higher operations. The first direction is connected with the cohomology of Lie algebras and theory representations. second main theme at intersection toric topology, homotopy polyhedral products, homology local rings, Stanley–Reisner rings simplicial complexes.

Abstract Let k be a field and $$R=k[x_1,\ldots ,x_n]/I=S/I$$ R = k [ x 1 , … n ] / I S</mml:m...

We give an introduction to the theory of determinantal ideals and rings, their Gröbner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras. Let K be a field and X an m × n matrix of indeterminates...

in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.