TY - CHAP
T1 - On Weak Hypervector Spaces Over a Hyperfield
AU - Panjarike, Pallavi
AU - Kuncham, Syam Prasad
AU - Al-Tahan, Madeleine
AU - Bhatta, Vadiraja
AU - Panackal, Harikrishnan
N1 - Funding Information:
Acknowledgements The authors express their deep gratitude to the referee(s)/editor(s) for their careful reading of the manuscript, and valuable suggestions that have definitely improved the paper. The first author acknowledges the Manipal Academy of Higher Education, Manipal, for providing the scholarship under Dr T M A Pai Fellowship. All the authors thank the Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, for their kind encouragement. The author Madeleine Al-Tahan acknowledges Abu Dhabi University, UAE. The first author thanks the organizers of ICLAA-2021 for providing an opportunity to present the talk.
Funding Information:
The authors express their deep gratitude to the referee(s)/editor(s) for their careful reading of the manuscript, and valuable suggestions that have definitely improved the paper. The first author acknowledges the Manipal Academy of Higher Education, Manipal, for providing the scholarship under Dr T M A Pai Fellowship. All the authors thank the Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, for their kind encouragement. The author Madeleine Al-Tahan acknowledges Abu Dhabi University, UAE. The first author thanks the organizers of ICLAA-2021 for providing an opportunity to present the talk.
Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
PY - 2023
Y1 - 2023
N2 - Hypervector spaces over a hyperfield are the generalized vector spaces in which at least one operation is taken as a hyperoperation. In this paper, we provide intriguing examples and counter-examples that highlight the importance of weak hypervector spaces. Moreover, we establish the properties of subhyperspaces, direct sums, and isomorphism theorems between hypervector spaces. Also, we explore the structural aspects of weak hypervector spaces, in particular, in the case of dual spaces. Furthermore, we prove the dimension condition dim (U) + dim (Uo) = dim (V) for annihilators in hypervector spaces.
AB - Hypervector spaces over a hyperfield are the generalized vector spaces in which at least one operation is taken as a hyperoperation. In this paper, we provide intriguing examples and counter-examples that highlight the importance of weak hypervector spaces. Moreover, we establish the properties of subhyperspaces, direct sums, and isomorphism theorems between hypervector spaces. Also, we explore the structural aspects of weak hypervector spaces, in particular, in the case of dual spaces. Furthermore, we prove the dimension condition dim (U) + dim (Uo) = dim (V) for annihilators in hypervector spaces.
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U2 - 10.1007/978-981-99-2310-6_22
DO - 10.1007/978-981-99-2310-6_22
M3 - Chapter
AN - SCOPUS:85167918035
T3 - Indian Statistical Institute Series
SP - 435
EP - 460
BT - Indian Statistical Institute Series
PB - Springer Science and Business Media B.V.
ER -