R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.

BACKGROUND Reports of the use of brainstem auditory evoked response (BAER) as a diagnostic modality in foals have been limited. HYPOTHESIS/OBJECTIVES To describe BAER findings and associated causes of hearing loss in foals. ANIMALS Study group 18 foals (15 neonatal, 3 nonneonatal), control group (5 neonatal foals). METHODS Retrospective. BAER records from the Clinical Neurophysiology Labo...

Theorem: An AW*-algebra is the ring generated by its projections if and only if it has no abelian summand. Corollary: Every equivalence in an A W*-algebra may be implemented by a partial isometry in the ring generated by the projections of the algebra. The corollary is extended to certain finite Baer »-rings. An early proposition in the theory of von Neumann algebras is that every such algebra ...

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

We show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. Hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. As aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. This generalizes and simplifies a result of  Dung and   Smith. As another consequen...

In this paper we define Baer BL-algebras as BL-algebras with the property that co-annihilator filters are generated by central elements. We use sheaf-theoretic techniques to construct a Baer extension of any BLalgebra, that is to embed any nontrivial BL-algebra A into a Baer BLalgebra A∗. The embedding turns to be an isomorphism if A is itself a Baer BL-algebra. 2000 MSC: 08A72, 03G25, 54B40, 0...

OBJECTIVE To determine the initial Brainstem Auditory Evoked Response (BAER) abnormalities in neonates with hyperbilirubinemia and the possible reversibility of abnormal BAER after therapy. DESIGN Prospective cohort study. SETTING Tertiary care hospital. SUBJECTS 30 term neonates with hyperbilirubinemia (S. bilirubin < 15 mg/dl) as cases and 25 normal term neonates as controls. METHODS ...

Best known for his contributions to the field of embryology [6], Karl Ernst von Baer [5] also pursued a variety of other areas of study including medicine, botany, zoology, and anthropology. Committing his life to scientific research, von Baer?s work led to the advancement of the understanding of mammalian reproduction, development, and organ functioning. His embryological discoveries ultimatel...

Introduction. A module over a ring will be said to be locally projective if and only if every finitely generated submodule is projective. As will be shown (7.14), it readily follows from known facts that if M is a locally projective module over a regular ring R, then the set L(M, R) of all finitely generated submodules of M is a relatively complemented modular lattice. This paper is concerned w...