Boyadzhiev, Khristo N.
Published in
Discussiones Mathematicae - General Algebra and Applications

In this paper, we discuss sums of powers 1p + 2p + + np and compute both the exponential and ordinary generating functions for these sums. We express these generating functions in terms of exponential and geometric polynomials and also show their connection to other interesting series. In particular, we show their connection to an interesting probl...

Lee, Edmond W.H.
Published in
Discussiones Mathematicae - General Algebra and Applications

A nontrivial pseudovariety is join irreducible if whenever it is contained in the complete join of some collection of pseudovarieties, then it is contained in one of the pseudovarieties. A finite semigroup is join irreducible if it generates a join irreducible pseudovariety. The present article is concerned with semigroups that are 2-testable in th...

Arabyani, Homayoon Sadeghifard, Mohammad Javad
Published in
Discussiones Mathematicae - General Algebra and Applications

In this paper, we present the concept of isoclinism of Lie algebras and its relationship to the Schur multiplier of Lie algebras. Moreover, we prove some properties of a pair of nilpotent Lie algebras.

Sundarayya, P. Kishore, T. Ravi
Published in
Discussiones Mathematicae - General Algebra and Applications

The notion of modular and distributive posets which generalize the corresponding notions from the lattice theory are introduced by J. Larmerova and J. Rachnek. Later some extended results of uniquely complemented lattice are derived to uniquely complemented posets. Now, in this paper, some equivalent conditions for a poset to be modular poset are g...

Rao, Marapureddy Murali Krishna
Published in
Discussiones Mathematicae - General Algebra and Applications

In this paper, as a further generalization of ideals, we introduce the notion of tri-quasi ideal as a generalization of ideal, left ideal, right ideal, bi-ideal, quasi ideal, interior ideal, bi-interior ideal,weak interior ideal, bi-quasi ideal, tri-ideal,quasi-interior ideal and bi-quasi-interior ideal of Γ-semiring. Some charecterizations of Γ-se...

Mozumder, Muzibur Rahman Dar, Nadeem Ahmad Khan, Mohammad Salahuddin Abbasi, Adnan
Published in
Discussiones Mathematicae - General Algebra and Applications

Let R be a ring with involution ′∗′. The skew Lie product of a, b ∈ R is defined by ∗[a, b] = ab − ba∗. The purpose of this paper is to study the commutativity of a prime ring which satisfies the various ∗-differential identities involving skew Lie product. Finally, we provide two examples to prove that the assumed restrictions on some of our resul...

Kehayopulu, Niovi
Published in
Discussiones Mathematicae - General Algebra and Applications

A poe-semigroup is a semigroup S at the same time an ordered set having a greatest element “e” in which the multiplication is compatible with the ordering. A ∨e-semigroup is a semigroup S at the same time an upper semilattice with a greatest element “e” such that a(b ∨ c) = ab ∨ ac and (a ∨ b)c = ac ∨ bc for every a, b, c ∈ S. If S is not only an u...

Chalapathi, Tekuri Sajana, Shaik
Published in
Discussiones Mathematicae - General Algebra and Applications

Let R be a finite commutative ring with unity. In this paper, we consider set of additive and mutual additive inverses of group units of R and obtain interrelations between them. In general φ(Zn) is even, however we demonstrate that φ(R) is odd for any finite commutative ring with unity of Char(R) ≠ 2. Further, we present unitary invertible graph r...

Rahaman, Md Hamidur
Published in
Discussiones Mathematicae - General Algebra and Applications

Let R be a noncommutative prime ring of char (R) ≠ 2, F a generalized derivation of R associated to the derivation d of R and I a nonzero ideal of R. Let S ⊆ R. The left annihilator of S in R is denoted by lR(S) and defined by lR (S) = {x ∈ R | xS = 0}. In the present paper, we study the left annihilator of the sets {F (x)◦n F (y)−x◦n y | x, y ∈ I}...

Belsi, G. Gold Kavitha, S. Selvakumar, K.
Published in
Discussiones Mathematicae - General Algebra and Applications

Let R be a finite commutative ring with identity. The idempotent graph of R is the simple undirected graph I(R) with vertex set, the set of all nontrivial idempotents of R and two distinct vertices x and y are adjacent if and only if xy = 0. In this paper, we have determined all isomorphism classes of finite commutative rings with identity whose I(...