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Displaying 61 – 80 of 181

Left EM rings

Jongwook Baeck (2024)

Czechoslovak Mathematical Journal

Let $R [x]$ be the polynomial ring over a ring $R$ with unity. A polynomial $f (x) \in R [x]$ is referred to as a left annihilating content polynomial (left ACP) if there exist an element $r \in R$ and a polynomial $g (x) \in R [x]$ such that $f (x) = r g (x)$ and $g (x)$ is not a right zero-divisor polynomial in $R [x]$ . A ring $R$ is referred to as left EM if each polynomial $f (x) \in R [x]$ is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions. Moreover,...

Locally compact Baer rings.

Ursul, Mihail (2004)

Acta Universitatis Apulensis. Mathematics - Informatics

Maximal quotient rings and essential right ideals in group rings of locally finite groups.

Ferrán Cedó, Brian Hartley (1992)

Publicacions Matemàtiques

Let k be a commutative field. Let G be a locally finite group without elements of order p in case char k = p > 0. In this paper it is proved that the type I∞ part of the maximal right quotient ring of the group algebra kG is zero.

Modules whose countably generated submodules are epimorphic images

O. A. S. Karamzadeh (1982)

Colloquium Mathematicae

Modules with semiregular endomorphism rings

Kunio Yamagata (2008)

Colloquium Mathematicae

We characterize the semiregularity of the endomorphism ring of a module with respect to the ideal of endomorphisms with large kernel, and show some new classes of modules with semiregular endomorphism rings.

Near-rings in which each prime factor is simple.

Birkenmeier, Gary F., Groenewald, Nico J. (1999)

Mathematica Pannonica

Near-rings with a special condition on idempotents.

Heatherly, H.E., Courville, J.R. (1999)

Mathematica Pannonica

New characterizations of von Neumann regular rings and a conjecture of Shamsuddin.

Carl Faith (1996)

Publicacions Matemàtiques

A theorem of Utumi states that if R is a right self-injective ring such that every maximal ideal has nonzero annihilator, then R modulo the Jacobson radical J is a finite product of simple rings and is a von Neuman regular ring. We prove two theorems and a conjecture of Shamsuddin that characterize when R itself is a von Neumann ring, using a splitting theorem of the author on when the maximal regular ideal of a ring splits off.

Nil-extensions of completely simple semirings

Sunil K. Maity, Rituparna Ghosh (2013)

Discussiones Mathematicae - General Algebra and Applications

A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.