In the case that X,Y are projective, nonsingular curves and φ is nonconstant, we already know that φ is necessarily surjective, but we will prove (more accurately, sketch a proof of) a much stronger result. From now on, for convenience, when we speak of the local ring of a nonsingular curve as being a discrete valuation ring, we assume that the valuation is normalized so that there is an elemen...

in this paper, for a complete lattice l, we introduce interval-valued l-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. some characterization and properties are discussed.

Let R be a local ring of bounded module type. It is shown that R is an almost maximal valuation ring if there exists a non-maximal prime ideal J such that R/J is an almost maximal valuation domain. We deduce from this that R is almost maximal if one of the following conditions is satisfied: R is a Q-algebra of Krull dimension ≤ 1 or the maximal ideal of R is the union of all non-maximal prime i...

We investigate Hermitian forms on finitely generated torsion modules over a noncommutative discrete valuation ring. We also give some results for lattices, which still are satisfied even if the base ring is not commutative. Moreover, for a noncommutative discrete-valued division algebra D with valuation ring R and residual division algebra D̄, we prove that W(D̄) ∼=WT(R), where WT(R) denotes the ...

Normal toric varieties over a field or a discrete valuation ring are classified by rational polyhedral fans. We generalize this classification to normal toric varieties over an arbitrary valuation ring of rank one. The proof is based on a generalization of Sumihiro’s theorem to this non-noetherian setting. These toric varieties play an important role for tropicalizations. 2010 Mathematics Subje...

In this paper, for a complete lattice L, we introduce interval-valued L-fuzzy ideal (prime ideal) of a near-ring which is an extended notion of fuzzy ideal (prime ideal) of a near-ring. Some characterization and properties are discussed.

in this paper, we apply the biswas’ idea of anti fuzzy subgroups toideals of near-rings. we introduce the notion of anti fuzzy ideals of near-rings,and investigate some related properties.

valuation is one of the main subjects in investment management which plays an important role in efficient capital allocation. valuation has become an important subject since supreme leader addressed the 44th principal of constitutional law. considering many problems which have arrised in valuation and stock pricing by privatization organization during resent years,it is essential to pay more at...