Epimorphisms, dominions and seminormal identities II

We associate two natural numbers with a seminormal identity depending on the first and the last occurrences of two two-letter subwords of the left hand side which are not subwords of its right hand side. Using these natural numbers, we find some classes of heterotypical identities where both sides contain repeated variables that are preserved under epis in conjunction with a seminormal identity.     

Epimorphisms,dominions and semigroups

We investigate the preservation of epimorphism-related properties of semigroups under the taking of morphic images, of ideals and adjunction of an identity.Presented by Boris M. Schein.     

Epimorphisms, dominions and permutative semigroups

We show that any right semicommutative semigroup satisfying the minimum condition on principal right ideals is saturated. Further we show that if a supersaturated semigroup S has a globally idempotent ideal U which satisfies a nontrivial permutation identity $x_{1}x_{2}\ldots x_{n}=x_{i_{1}}x_{i_{2}}\ldots x_{i_{n}}We show that any right semicommutative semigroup satisfying the minimum condition on principal right ideals is saturated. Further we show that if a supersaturated semigroup S has a globally idempotent ideal U which satisfies a nontrivial permutation identity x₁x₂?x_n=x_i1x_i2?x_inx_{1}x_{2}\ldots x_{n}=x_{i_{1}}x_{i_{2}}\ldots x_{i_{n}} such that i ₁=1 and i _n ≠n, then U is also supersaturated.     

Epimorphisms,dominions and $$mathcal {H}$$H-commutative semigroups

Semigroup Forum - In the present paper, a series of results and examples that explore the structural features of $$mathcal {H}$$-commutative semigroups are provided. We also generalize a result of...     

Epimorphisms and ℋ-coextensions

Conclusions Theorems 3.4 and 4.3 have consequences of a similar form: we have compact monoids built from objects in a smaller category of compact monoids, and an epimorphism in the larger category is surjective provided the induced morphism (in 3.4 the restriction to the idempotents) is surjective. In 3.2 and 3.3 we make use of the fact that for the smaller category CL this will always be the case. Thus 3.4 and 4.3 could be completed, in a sense, if we know more about epimorphisms of compact semilattices and about A-epimorphisms. As for 3.4, another type of completion would be an extension to the nonabelian case. Since it is not known (see [2], [17]) whether constructions analogous to those in 3.1 yield Hausdorff semi-groups for the non-Lawson case, this problem may be difficult.In closing, the author would like to thank Professor J. H. Carruth for his helpful advice and encouragement in the research leading to this paper.     

Natural Classes,Left Exact Preradicals,and Flat Epimorphisms

We define a function between the lattice of left exact preradicals in R-mod and the complete boolean lattice R-nat of natural classes in R-mod in such a way that the image of this function results to be a complete sublattice of R-nat. The image of this function is R-nat if and only if R is left semiartinian. We prove that every flat ring epimorphism from R to S induces a function between the lattice of left exact preradicals in R-mod and the lattice of left exact preradicals in S-mod. In this context, we obtain a lattice decomposition of S-nat for each left exact preradical.     

Normal and seminormal eigenvalues of matrix functions

LetP() be ann×n analytic matrix function andW(P) be its numerical range. In this paper classical results on the normality of matrix eigenvalues on W(P) are generalized to the context of such matrix functions. Special attention is paid to corners of W(P) and to the special case of matrix polynomialsP().     

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 con-sequence, 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, _A B 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.     

Small sublattices with large dominions

Two examples of finite sublattices with infinite dominions are given. It is proven that this cannot occur in a finitely generated lattice variety. Received May 10, 2001; accepted in final form October 6, 2005.     

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.