Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

Let $R$ be a ring and $M$ a right $R$-module with $S=End_R(M)$. A module $M$ is called semi-projective if for any epimorphism $f:Mrightarrow N$, where $N$ is a submodule of $M$, and for any homomorphism $g: Mrightarrow N$, there exists $h:Mrightarrow M$ such that $fh=g$. In this paper, we study SGQ-projective and $pi$-semi-projective modules as two generalizations of semi-projective modules. A ...

A quojection (projective limit of Banach spaces with surjec-tive linking mappings) without infinite dimensional Banach subspaces is constructed. This results answers a question posed

Let F be a field, let D be a subring of F , and let X be the Zariski-Riemann space of valuation rings containing D and having quotient field F . We consider the Zariski, inverse and patch topologies on X when viewed as a projective limit of projective integral schemes having function field contained in F , and we characterize the locally ringed subspaces of X that are affine schemes.

We describe a method to try to construct non-Desarguesian projective planes of a given finite order using a computer program. If a projective plane of order n exists, then it can be constructed from a dual linear space by a sequence of one-line extensions. We analyze this extension process, and find a criterion to limit the search for possible extensions. Up to isomorphism, there are 105 dual l...

We analyze the spectrum of a self-adjoint operator on a Laakso space using the projective limit construction originally given by Barlow and Evans. We will use the hierarchical cell structure induced by the choice of approximating quantum graphs to calculate the spectrum with multiplicities. We also extend the method for using the hierarchical cell structure to more general projective limits bey...

We prove that any affine, resp. polarized projective, spherical variety admits a flat degeneration to an affine, resp. polarized projective, toric variety. Motivated by Mirror Symmetry, we give conditions for the limit toric variety to be a Gorenstein Fano, and provide many examples. We also provide an explanation for the limits as boundary points of the moduli space of stable pairs whose exist...

In this note, we make two nonstandard group-theoretic observations. First, we give a short nonstandard proof of a well-known result in group theory concerning locally nilpotent groups. Second, we outline a nonstandard way of viewing the projective limit of an projective family of groups. (We are unsure if this second observation, in some form, has already been discovered, although we would not ...