Lb-coequalizers and Lb-regular Epimorphisms in the Category of L-sets and Bi-induced Maps

In this paper,it gives the definition of the category of ■-sets and bi-induced maps whose true value set is a Locale,a complete Heyting algebra.In this category it defines the L_b-monomorphisms and the L_b-epimorphisms.Especially,it gives the definition,the judgmental theorem of L_b-coequalizers.Furthermore,it defines L_b-regular epimorphisms and proves the judgmental theorem.At the end it concludes a result:the category of ■-sets and bi-induced maps is finitely cocomplete.

Epimorphisms between Finite 4-Valued Modal Algebras

In this paper, we determine conditions for the existence of an epimorphism between two finite 4-valued modal algebras and state a method to obtain it. Furthermore, we obtain formulas which generalize those indicated by R. Sikorski for finite Boolean algebras [1] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100310038000000 , and by M. Abad and A. V. Figallo for finite 3-valued ukasiewicz algebras [2] 08D0C9EA79F9BACE118C8200AA004BA90B02000000080000000E0000005F005200650066003300380037003200340036003100320031000000 .

Homological Epimorphisms, Compactly Generated t-Structures and Gorenstein-Projective Modules

The aim of this paper is two-fold.Given a recollement(T′,T,T′′,i*,i_*,i~!,j!,j*,j*),where T′,T,T′′are triangulated categories with small coproducts and T is compactly generated.First,the authors show that the BBD-induction of compactly generated t-structures is compactly generated when i*preserves compact objects.As a consequence,given a ladder(T′,T,T′′,T,T′) of height 2,then the certain BBD-induction of compactly generated t-structures is compactly generated.The authors apply them to the recollements induced by homological ring epimorphisms.This is the first part of their work.Given a recollement(D(B-Mod),D(A-Mod),D(C-Mod),i*,i_*,i~!,j!,j*,j_*) induced by a homological ring epimorphism,the last aim of this work is to show that if A is Gorenstein,AB has finite projective dimension and j! restricts to D^b(C-mod),then this recollement induces an unbounded ladder(B-Gproj,A-Gproj,C-Gproj) of stable categories of finitely generated Gorenstein-projective modules.Some examples are described.

Localization of homotopy epimorphisms and homotopy monomorphisms

Recall that f: X→Y is a homotopy epimorphism (monomorphism), if given u, v: Y→W (u, v: W→X), uofvof implies uv (foufov implies uv). In this note, we shall consider the localization of homotopy epimorphisms andmonomorphism, 1.e. the following is considered. Problem. If f:X→Y is a homotopy epimorphism (monomorphism), then is any

Generalized Hopfian Property, a Minimal Haken Manifold, and Epimorphisms Between 3-Manifold Groups

We address the question that if π_1-surjective maps between closed aspherical 3-manifolds have the same rank on π_1 they must be of non-zero degree. The positive answer is proved for Seifert manifolds, which is used in constructing the first known example of minimal Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3- manifolds. Many examples are given.

S-SUPERFLUOUS AND S-ESSENTIAL HOMOMORPHISMS

Let R be a ring and S a class of R-modules. S-superfluous epimorphisms and S-essential monomorphisms are introduced and studied in this article. As applications, some new characterizations of von Neumann regular rings and perfect rings are given. Finally, these notions are also used to study minimal homomorphisms.

Minimal silting modules and ring extensions

Ring epimorphisms often induce silting modules and cosilting modules,termed minimal silting or minimal cosilting.The aim of this paper is twofold.Firstly,we determine the minimal tilting and minimal cotilting modules over a tame hereditary algebra.In particular,we show that a large cotilting module is minimal if and only if it has an adic module as a direct summand.Secondly,we discuss the behavior of minimality under ring extensions.We show that minimal cosilting modules over a commutative noetherian ring extend to minimal cosilting modules along any flat ring epimorphism.Similar results are obtained for commutative rings of small homological dimensions.

Deer antler renewal gives insights into mammalian epimorphic regeneration

Deer antlers are the only known mammalian organ that,once lost,can fully grow back naturally.Hence,the antler offers a unique opportunity to learn how nature has solved the problem of mammalian epimorphic regeneration(EpR).Comprehensive comparisons amongst different types of EpR reveal that antler renewal is fundamentally different from that in lower vertebrates such as regeneration of the newt limb.Surprisingly,antler renewal is comparable to wound healing over a stump of regeneration-incompetent digit/limb,bone fracture repair,and to a lesser extent to digit tip regeneration in mammals.Common to all these mammalian cases of reaction to the amputation/mechanical trauma is the response of the periosteal cells at the distal end/injury site with formation of a circumferential cartilaginous callus(CCC).Interestingly,whether the CCC can proceed to the next stage to transform to a blastema fully depends on the presence of an interactive partner.The actual form of the partner can vary in different cases with the nail organ in digit tip EpR,the opposing callus in bone fracture repair,and the closely associated enveloping skin in antler regeneration.Due to absence of such an interactive partner,the CCC of a mouse/rat digit/limb stump becomes involuted gradually.Based on these discoveries,we created an interactive partner for the rat digit/limb stump through surgically removal of the interposing layers of loose connective tissue and muscle between the resultant CCC and the enveloping skin after amputation and by forcefully bonding two tissue types tightly together.In so doing partial regeneration of the limb stump occurred.In summary,if EpR in humans is to be realized,then I envisage that it would be more likely in a manner akin to antler regeneration rather to that of lower vertebrates such as newt limbs.