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51.
Let S be a regular semigroup and E(S) be the set of its idempotents. We call the sets S(e, f)f and eS(e, f) one-sided sandwich sets and characterize them abstractly where e, fE(S). For a, a′ ∈ S such that a = aa′a, a′ = a′aa′, we call S(a) = S(a′a, aa′) the sandwich set of a. We characterize regular semigroups S in which all S(e; f) (or all S(a)) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural order. For every aS, we also define E(a) as the set of all idempotets e such that, for any congruence ϱ on S, aϱa 2 implies that aϱe. We study the restrictions on S in order that S(a) or be trivial. For , we define on S by a b if . We establish for which S are or congruences.  相似文献   
52.
The class \({\mathcal{CR}}\) of completely regular semigroups equipped with the unary operation of inversion forms a variety whose lattice of subvarieties is denoted by \({\mathcal{L(CR)}}\). The variety \({\mathcal B}\) of all bands induces two relations \({\mathbf{B}^{\land}}\) and \({\mathbf{B}^{\lor} }\) by meet and join with \({\mathcal B}\). Their classes are intervals with lower ends \({\mathcal V_{B^{\land}}}\) and \({\mathcal V_{B^{\lor}}}\), and upper ends \({\mathcal V^{B^{\land}}}\) and \({\mathcal V^{B^{\lor}}}\). These objects induce four operators on \({\mathcal{L(CR)}}\).The cluster at a variety \({\mathcal V}\) is the set of all varieties obtained from \({\mathcal V}\) by repeated application of these four operators. We identify the cluster at any variety in \({\mathcal{L(CR)}}\).  相似文献   
53.
We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.  相似文献   
54.
The translational hull in semigroups and rings   总被引:4,自引:0,他引:4  
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55.
Summary For a commutative cancellative semigroup S, we define the rank of S intrinsically. This definition implies that the rank of S equals the usual rank of its group of quotients. We also characterize the rank in terms of embeddability into a rational vector space of the greatest power cancellative image of S.  相似文献   
56.
Hedrlin and Pultr proved that every small category is isomorphic to a full subcategory of the category Alg (Δ) of all algebras of type Δ whenever the sum ∑Δ of their arities satisfies ∑Δ>2. This article deals with simultaneous representation in categories of algebras, a generalization of the related question: given a subcategory k′ of a small category k, when does there exist an extension Δ′ of a type Δ with ∑Δ?2 such that k′ is a full subcategory of Alg(Δ′) while the Alg (Δ)-redacts of algebras representing k′ determine a category isomorphic to k? We characterize simultaneous representability by algebras and their reducts completely, and show that it is closely related to Isbell's dominion. A consequence of the main result states that algebraically representable pairs (k′, k) of one-object categories k′ k are exactly those for which k′ coincides with its dominion in k, and provides an alternative characterization of the dominion. Simultaneous representability by partial algebras is not subject to any such restriction.  相似文献   
57.
Algebra universalis - Completely simple semigroups form a variety if we consider them as algebras with multiplication and inversion. A near variety of idempotent generated completely simple...  相似文献   
58.
59.
Lipofuscin is a yellow-brown, highly fluorescent pigment that undergoes an age-related progressive accumulation in animal cells, mainly in postmitotic cells. It is a heterogeneous, high-molecular weight material associated with proteins, lipids and nucleic acids. Lipofuscin is implicated in many aspects of human health, including aging, oxidative stress, macular degeneration, lipid peroxidation, atherosclerosis, dementia (Alzheimer's Disease) and diseases associated with prions. Although the fluorescent properties of lipofuscin have long been recognized, neither histologists nor chemists have yet isolated the pigments themselves or characterized their optical properties. We have prepared lipofuscinlike species by reacting malondialdehyde (MDA) with cysteine (Cys). MDA:Cys adducts 3:2 and 2:2 are two of those that have been identified among the many that were present in the reaction. Whereas previous attempts to synthesize lipofuscinlike species resulted in compounds that were either nonfluorescent or emitted principally in the blue, the MDA:Cys adducts reported in this study are not only fluorescent but also emit over a broader range.  相似文献   
60.
Let be the set of nonnegative integers and the ring of integers. Let be the ring of N × N matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of all matrices in with only a finite number of nonzero entries and the subring of generated by the identity matrix. Regular elements are also described. We characterize all ideals of , show that all ideals are finitely generated and that not all ideals of are principal. Some general ring theoretic properties of are also established.  相似文献   
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