Related papers: Morphic elements in regular near-rings
'A semigroup is completely regular if and only if it is a union of groups'- an analogue of this structure theorem of completely regular semigroup has been obtained in the setting of seminearrings in [[16], Mukherjee (Pal) et al., Semigroup…
In this article several properties of the inverse along an element will be studied in the context of unitary rings. New characterizations of the existence of this inverse will be proved. Moreover, the set of all invertible elements along a…
We introduce the notions of one-sided dirings, 3-irreducible left modules, 3-primitive left dirings, 3-semi-primitive left dirings, 3-primitive ideals and 3-radicals. The main results consists of two parts. The first part establishes two…
We consider rings whose one-sided ideals are close to automorphism-invariant modules. We study rings in which every (finitely generated) right ideal is automorphism invariant and rings in which every right ideal is a finite direct sum of…
A near-group category is an additively semisimple category with a product such that all but one of the simple objects is invertible. We classify braided structures on near-group categories, and give explicit numerical formulas for their…
The concepts of localizable set, localization of a ring and a module at a localizable set are introduced and studied. Localizable sets are generalization of Ore sets and denominator sets, and the localization of a ring/module at a…
We study homomorphisms of Hecke monoids, notably parabolic homomorphisms, which map parabolic elements to parabolic elements, and injective ones. The importance of the first class stems from the fact that parabolic elements form a rather…
We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties,…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…
We give a survey of results on the structure of right and left Engel elements of a group. We also present some new results in this topic.
Let $R$ be a commutative ring of characteristic zero and $G$ an arbitrary group. In the present paper we classify the groups $G$ for which the set of symmetric elements with respect to the classical involution of the group ring $RG$ is Lie…
In what follows we generalize the notion of a complemented ring to rings that are not necessarily reduced. We then determine how our concepts fit in with other well-known classes of rings.
We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more explicit description of the quadratic forms of the…
In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…
We introduce the notion of solid monoid and rigid monoid in monoidal categories and study the formal properties of these objects in this framework. We show that there is a one to one correspondence between solid monoids, smashing…
Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…
We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.
We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
This paper introduces and studies the higher-order group inverse in a ring. We extend known properties of the higher-order group inverse from complex matrices to elements of a ring and, in the process, derive new results. We further…