• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.433-441
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• 2005

The concepts linearly independent elements and u-linearly independent elements in an N-group G where N is a near-ring, were introduced and studied. A few important results in the theory of vector spaces were generalized to N-groups.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.847-853
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• 1999

The purpose of this paper is to develop the theory of coassociated primes and to investigate Melkersson's question [8].

• East Asian mathematical journal
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• v.21 no.2
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• pp.205-217
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• 2005

In this paper we consider the fuzzy ideals of N-group G where N is a near-ring. We introduce the concepts: minimal elements, fuzzy linearly independent elements, and fuzzy basis of an N-group G and obtained fundamental related results.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.401-417
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• 2017

Ever since their introduction, skew PBW ($Poincar{\acute{e}}$-Birkhoff-Witt) extensions of rings have kept growing in importance, as researchers characterized their properties (such as primeness, Krull and Goldie dimension, homological properties, etc.) in terms of intrinsic properties of the base ring, and studied their relations with other fields of mathematics, as for example quantum mechanics theory. Many rings and algebras arising in quantum mechanics can be interpreted as skew PBW extensions. Our aim in this paper is to study skew PBW extensions of Baer, quasi-Baer, principally projective and principally quasi-Baer rings, in the case when the base ring R is not assumed to be reduced. We just impose some mild compatibleness over the base ring R, and prove that these properties are stable over this kind of extensions.